Deku got the quirks that the past OFA quirk user had (not including OFA). How come All Might didn't get them also?
My guess is All Might might have stopped after having power to beat any type of enemies and he didn't even get to think of the future that at someday he might lose his power or maybe he understood the power given by his mentor whereas Deku wanted to learn where this power comes from and what can make him more powerful... More like that power generates from emotion and doubt
Because when All Might gave Deku the quirk One For All, it took his power. In episode 48, "Symbol of Peace", he lost it at the end of the episode.
And it's explained in episode 98, "That Which is Inherited", that the quirks of the previous One For All users have mixed in with its core, and they will unlock over time. He's told that he will unlock six quirks in total, starting with "Blackwhip" which appeared in that episode. And when it got passed on, Deku inherited all of One For All's power.
I think its because he was chosen to be the one to manifest the quirks. The vestiges probably came to that decision. Nana Shimura was told that it wasn't time yet. However, Deku was told that the time was ripe. That probably means that all the vestiges came to the decision that the 9th user (Deku) was the right one to manifest the quirks. This could be because he is a great user and they agreed with All Might's choice to choose him, or because the villains are making their move and the current generation needs a strong hero.
Most likely, it was just a matter of timing. There is a lot of textual evidence for this. I suggest reviewing episodes 98, 100, 123, and 130 to learn more about the vestiges, One For All, and All For One.
The Full Manifestation Took Time
In Episode 100 - The New Power and All For One, All Might, Midoriya, and Bakugo speculate on why the new power manifested and make some comments. All Might notes,
"One for All's power is growing."
And Midoriya states that when the power manifested, the Dark Whip user said,
"The time is ripe."
In Episode 123 - The Ones Within Us the vestiges note that Midoriya does not have a full form in the world of One For All, as that takes time.
In Episode 131 - Izuka Midoriya and Tomura Shikaraki, the first user states
"Before, we could only involve ourselves in the spaces between fluctuations, but we're not limited to that anymore. Because about four months ago, my power--One For All--suddenly started to grow rapidly. Along with that growth, the previous wielders inside One For All were able to take on shape and communicate with each other."
Additionally, Midoriya's form is shown to have advanced enough that he can talk (mumble, really, as his mouth is only partially formed). This shows that with regards to One For All, some aspects of it take time, whether it be manifesting as a vestige or manifesting the previous users' Quirks. The main reason All Might didn't manifest the previous user's Quirks was probably just that not enough time had passed.
In Episode 98 - That Which is Inherited, the vestige of the Blackwhip user gives some explanation on what's happening:
"Our Quirk factors are mixed in with the core of the power--the tiny core that's always been part of One For All. A tiny spot in the middle of flickering flames, or the surface of billowing waves. The origin of the power is wrapped in the cultivated power. Right now, it's becoming larger and starting to move. What you saw between fluctuations... One For All itself... is growing."
Here is yet another instance of someone stating One For All is growing. One For All, the Quirk that allows users to stockpile strength and pass it on, seems to further develop over a period of time. The Blackwhip user further states that Blackwhip has grown in power while inside of One For All, which suggests this power too was developing whilst in the core of One For All, over a period of time.
In this episode, we also see that Nana Shimura was told "The time has not yet come." when she received the power. In one of the episodes I skimmed, I saw it implied (probably by All Might) that Shimura did not even know the Quirks of the previous users were stored in One For All. And this is corroborated by one of the users saying he used his power to hide, and built up strength via training, in order to stockpile it and pass it to the next user--implying they thought the main purpose of One For All was passing along physical strength, not Quirks.
A Quirkless User Might Be A Prerequisite
In episode 131, the vestiges talk a lot about One For All and there are some shocking revelations, such as that one of the users died of old age at only age 40, likely due to having multiple Quirks. They conclude that
"One For All cannot be used by a normal human."
(Normal human is here defined as someone with a Quirk, since Quirkless people are now a rarity.)
They further state,
"[One For All] was able to have its true power drawn out by someone who did not have any power."
Something To Do With All For One
As stated, in episode 100, Bakugo, All Might, and Midoriya discuss why this might be happening. Bakugo asks if there was something that triggered it, but Midoriya answers,
"No, not at all. But he said, 'The time is ripe.'"
Speaking on external stimuli that may have triggered the change, they further speculate that the power manifesting had something to do with All For One. I do not recall the full context at this point in the story that would lead them to think this, but I guess Midoirya had some kind of contact with All For One.
Midoriya's Thoughts Triggered Blackwhip
In episode 98, the Blackwhip user implies his power manifested because Midoriya wanted it in that moment. Midoriya asks "Why? What's going to happen?" and he replies:
"You... Earlier, you thought,'I'll capture that guy,' right? You did, didn't you? The Quirk that works best for that is my Blackwhip."