Does Anyone Contemplate Using the Wish to Save All the Universes?
Neither the anime, nor the manga show any of the fighters contemplate using the wish to save all of the rest of the universes, nor is there any sort of collaboration to this end. There are a few instances of the wish being discussed. Most notably, this one in volume 7 of the manga comes closest:

It's very telling that the wolf guy says they need to figure out a way everyone can survive. This suggests that he does not currently know a way all the universes can survive. Even though it may seem obvious to us to use the wish from the Super Dragon Balls, it evidently is not to this guy. Piccolo does not have a response either.
There are several other times when a wish is discussed. 17 for instance, wants a yacht. And it is confirmed in the manga that Jiren would wish for the revival of his master. In exchange for his cooperation in fighting for Universe 6, Frieza asks Frost to use the wish to revive him (this is later shown to be a deception). In the anime, Vegeta suggests that he will use the wish for Universe 6.
Nobody says anything about saving all the universes.
There are four plausible conclusions here: either the fighters cannot even conceive of the idea of using the wish to save all the universes, the fighters cannot think of using the wish to save all the universes as a good idea, the fighters don't care about any universe but their own, or the narrative of Dragon Ball Super simply refuses to show us any fighters thinking about saving all the universes.
Thesis
Having established no one was shown to contemplate using the wish to save all the universes, it makes sense to try and determine why. As I will soon show, using the wish to undo the destruction of the universes is not as obvious as we might think.
There are many reasons why:
Out of Universe
- The narrative does not show anyone thinking this, even though some people might be thinking it, in order to retain tension during this story arc.
In Universe
- Making this wish would mean opposing the will of Grand Zeno, who wishes to reduce the number of universes.
- The majority of fighters are unfamiliar with the Dragon Balls, so they might not be capable of thinking to use them to restore all the universes.
- There is no trust amongst the universes and the fighters.
Out of Universe Explanation
A lot of the tension in this arc hinges on the fact that the universes are being culled. Up until the first one is completely obliterated, we wonder if Zeno is actually going to do it... and then he does.
As far as suspense goes, Dragon Ball Super inherited a very big narrative problem in the Dragon Balls. Time after time, the heroes have used their wishes to undo all the damage done by the bad guys. If that's the case, why should the audience worry about anything? The Dragon Balls make suspense very difficult. But the writers shouldn't totally give up on suspense, right? Thus, does it make sense to show any character contemplating wishing to restore all the universes ahead of time?
The answer is no. Once the audience is cued in that this is a possibility, the main source of tension is gone. The audience might wonder about it themselves, of course, which will make it frustrating to watch the tournament when the writers are deliberately avoiding talking about it at all. Still, whether or not it is truly a shock, the writers have to at least try to make 17's wish a surprise.
In Universe Explanations
Respect/Fear of the Gods
As the question points out, this whole situation doesn't seem make sense. With some reasoning and examination of the story, I will try to provide a framework where this situation makes sense. Perhaps this is just my opinion, but I believe we should try to believe a story makes sense until the author blunders and contradicts themselves so badly it cannot be rectified and is undoubtedly a plot hole. Thus, if there are frameworks where a story makes sense and frameworks where the story does not, then we must reject the frameworks where the story does not.
Thus, what it comes down to is this: while it would seem that a wish to restore all the universes should be obvious, under close scrutiny, it is not.
Zeno is the highest level god in the Dragon Ball multiverse. He is so powerful that all of the Destroyer Gods are afraid of him. And if Zeno truly is a being of which no greater can exist, then what he says is absolute and infallible. Whether or not this is actually true is not important. What is important is that many of the combatants will believe this.
The head angel (speaking on Zeno's behalf) states many times that the universes are going to be culled, that it is necessary, and that it is Zeno's will. Now, what does making a wish to undo Zeno's will amount to? It amounts to a rejection of his words and actions. Isn't that clearly the wrong thing to do? And if Zeno is the being who decides what is right and wrong, wouldn't it be immoral?
Consider the real world Abrahamic religions (Christianity, Islam, Judaism, etc), for instance. According to the tenets in these religions, there are no circumstances under which it is acceptable to defy the Abrahamic God. In their stories, God asks Abraham to sacrifice his son to him. The correct answer is not to say, "Hey, this is wrong, I'm not doing that." Rather, the correct answer is to comply, and in the end God will say, "Okay, you can stop; I was just testing you."
Apply this logic to the Dragon Ball multiverse. These two cases offer answers that are exact opposites. So Zeno wants the winner to openly go against his will to destroy all but one universe? How can he expect that when even the Destroyers are afraid to speak out against him? And how can that possibly be what's right when Zeno is an infallible deity? The angels stated multiple times that Zeno wished to cull the universes because there were too many. Honestly, if I were in the position to make that wish, I would simply assume if I used the wish to restore the universes, Zeno would just blow up every single one all over again, and this time the winning universe would be included.
I don't think it's an exaggeration to call Zeno a being of whose will is absolute. He can blow up an entire universe in an instant, so what else could he be, at least in the eyes of the mortals? Some or maybe even the majority of the fighters from the universes must think of him as an unstoppable and immutable force that shouldn't be tested. In fact, this very idea is stated over and over again in the manga and anime.
It is not unreasonable to think most of the fighters would think restoring the universes with the Super Dragon Balls was a bad idea. Over and over again, the deity characters state that Zeno is insurmountable. Going against Zeno is thus futile. And in the manga, we get this conversation between Whis and Goku from volume 6, page 68:
Goku: Yeah... Maybe I'll ask the Lord of Everything to call off this whole erasure thing.
Whis: I wouldn't do that if I were you. The Lord of Everything and the Grand Priest decided this. If you offend them, you'll just be erased.
What else do we know about Grand Zeno? Namely, that he thinks managing so many universes is a pain, and the endeavor seems pointless especially on account of their mortal levels not going up; thus, Zeno wants to get rid of some of the universes. This is shown directly in the manga between a conversation between him and the Grand Minister.
All this gives us these assumptions:
- Zeno wants to see a fighting tournament.
- Zeno wants less universes.
- Zeno cannot be opposed.
- If Goku suggests stopping the tournament or the erasure of universes, Zeno will be offended and destroy him.
From these, I would extrapolate this conclusion:
- If you undo the destruction of the universes, Zeno will be offended and destroy them all again, because as stated in 2, he does not want to manage so many universes.
At the very least, it is not unreasonable to think that the fighters are worried about this enough to think restoring the universes is not a viable option, or too risky. We should also question whether the fighters care enough about the other universes to risk their own in the event of their victory.
At best, Zeno's challenge is a riddle. To figure out what the correct wish is, one would have to put together the pieces: first, that perhaps the reason Zeno isn't the one saying anything is because the angels are not actually stating Zeno's will. And two, the reason that there are no restrictions on the wish is to use it to defy the destruction of every universe. But considering the destruction is in the first place being caused by the top-level god, who is supposed to determine what is good and moral, I don't think the answer to the riddle is obvious at all.
So to answer the question, I believe it is exceedingly likely that the majority of fighters did not plan on making a wish to restore all the universes if they won. Unless they have zero respect or fear for the gods (like Goku and 17), it would have been a difficult idea to even conceive of.
Evidence
I will preface with the following: fiction is a reflection of reality. Author and reader alike make default assumptions about a fictional world. Thus, ideas, even religious ones, will inevitably creep in. And indeed, though I started from a place of comparing Dragon Ball Super to real religions, I found plenty of the specific ideas I examined present in the work itself. Toriyama and Toyotarou's own views on the gods in their work can also be gleamed from this interview at the end of volume 4.

It's notable that they write the deities are just. This view would likely be reflected in their writing as well.
Since it has been rightfully questioned whether the people in the multiverse of Dragon Ball hold the proper reverence for their deities, I will try to examine the matter.
What I have is this: whether it's King Kai, Supreme Kai, or Beerus, the deities are constantly shocked at Goku's lack of respect. When Goku talks to Grand Zeno casually like they're buddies, Beerus has a total flip-out. This constant shock can only lead one to conclude that Goku's behavior is completely aberrant. The majority of the people in the multiverse would understand not to question gods.
Consider Vegeta and King Vegeta as well. When Beerus shows up, they both become groveling cowards to the point of becoming comic relief.
Another example comes from the manga in volume 9. We see the Namekians praying to their Dragon Ball, saying
It is thanks to the protection of the gods that we may live in peace. We mustn't forget to be grateful.
A quote from volume 8, just before Universe 10 gets obliterated:
Lord Gowas! I'm satisfied just to be carrying out the will of Universe 10's gods.
This all seems like a general adherence to the gods to me.
And here's a quote from Zamasu I found on https://dragonball.fandom.com/wiki/Zamasu
"You give corruption far too much credit, evil does not inform good. It sullies it, like how the Babari sullied their world with violence, or how that arrogant Goku sullied this sacred ground by swinging his fists at a God. Mortals receive the divine gift of intellect, the potential for wisdom, but they misuse it to destroy the beauty of creation. Mortals do not succumb to evil, they are the evil. They create it, and spread it with minds they shouldn't possess. How can we call ourselves gods if we watch this plight and do nothing to stop it?"
Here's a similar quote from chapter 19 of the manga (volume 3, page 152):
Zamasu/Goku Black: "In this universe right now... I reign supreme! Draaah!!!"
Vegeta: "We don't need a god who forces his own twisted sense of justice on us."
Zamasu/Goku Black: "Silence, you filthy mortal!! My reign is absolute! Every action that I, the supreme god, make... is justice!"
And from volume 4:


Zamasu is a bad guy, but these quotes and Zamasu's disgust with Goku shows that the idea that mortals are bad, and thus that gods are good and determine good, is not foreign to the world of Dragon Ball.
Additionally, in volume 4, the Supreme Kai gives some indication towards thinking it's a particularly egregious crime to kill a god:

Now, consider the fighters at the Tournament of Power. The most fervent believers in justice and love, such as Ribrianne and Toppo, have been questioned for seemingly not thinking of restoring all the universes with the wish. But oftentimes, the ones most dedicated to justice can be the ones most susceptible to blind obedience to higher authorities, including gods and angels, so I don't see this as contradictory. If Zeno is approving of what's happening, they might see the tournament as just, or they might simply see opposing Zeno as futile. Such thoughts will lead them away from contemplating this kind of wish.
We can see a bit of their trepidation in these panels from volume 7, so we know that their gods have told them enough about Grand Zeno.

Examining the final episode of the anime, Krillan and some others were shocked by 17's wish. It isn't really explained why, but we can assume either it was a surprising wish (nobody else could even conceive of it) or it was a dangerous wish (Grand Zeno might get mad).
Perhaps further evidence is the reason 17 makes the wish in the manga. As per volume 9, page 83:
Mostly, I just didn't want those little imps to have their way with things.
17 changes his wish to spite the two Grand Zenos. We see none of the "good" and "just" fighters even think of saving all the universes. The one person who actually makes the wish to restore all the universes is one with no fear or respect for the gods. And the Grand Priest bumps up Universe 7's mortal ranking for this, so evidently it is a good thing.
First Time Seeing Dragon Balls
We have to consider that for many of the fighters, this is their first time being told they can get a wish. Without the years of experience with Dragon Balls that Universe 7's heroes have, it might be difficult to even think of what that wish can be used for. I don't really have much to say about this reason, and the evidence is just that nobody seems to think of saving all the universes (see the picture at the beginning with the wolf guy).
The tournament also goes by pretty fast and is chaotic (at least in the manga, we get this impression), so a lot of the fighters might not even have a chance to stop and think. The spectators are enthralled in the match as well due to the fate of their universe being on the line.
One last point though: it is stated that there is no limitation on the wish, but there actually is one. It will be filtered through the Grand Priest, since it needs to be spoken in the language of the gods to Super Shenron. This is just another reason to be cautious with any wish. Did you want to wish Zeno destroyed to stop this from happening again? Whoops. Now you're in trouble.
Distrust Amongst the Universes
Another thing to consider is the level of trust between the universes. The gods and destroyers are all squabbling for survival, and not cooperating at all. It doesn't follow that the mortals would trust anyone from another universe to use the wish to restore theirs. Their distrust may even extend so far as to make them not want to restore any other universe. Regardless, there would be no cooperation; even someone contemplating making the wish, would not trust anyone else, and they would fight all the harder to make sure it's them who gets the prize.
We see Frieza making deals, but that's just him playing mind games, and it ends in backstabbing; that's because in the end, Frieza isn't going to trust his survival to the chance another universe would follow through on using the wish to revive him. It would be so easy not to once he's gone, after all. And that's true for any kind of deal regarding saving all the universes.
Some Frieza quotes from the manga:
Entrusting the fate of your universe to another? I've never heard something quite so pathetic.
Oh of course. In the heat of the battle, I forgot to mention some key advice. Never trust anyone!
Why even hesitate? This is a survival game, and our very existence is on the line. It seems I'm the only one here with a clear idea of how this is supposed to work.
The last one continues from the picture I included of Piccolo and the wolf guy. It just goes to show that even if some of the participants are willing to work together, it only takes one Frieza on the team for things to end in betrayal.
And a quote from Vegeta too:
Need me to hold your hands, child? Don't forget--in this arena, we're foes, so don't look to other universes for aid!