Since Katakuri can see the future, shouldn't speed and tricks be irrelevant? Did he just wear him out until he was susceptible to more emotions?
The fight between Luffy and Katakuri had many factors in play and has most of the fandom divided over its results. It wasn't a death match in the true sense, despite both sides struggling quite a bit. A lot of viewers are of the opinion that Katakuri was not truly defeated at the end, but rather chose to view Luffy as an equal and let him go.
In terms of raw power and control over the Devil Fruit, Katakuri outclassed Luffy by far. Even if Luffy could barely match the explosiveness of the attack with Gear Fourth, this places immense load on his body as Rayleigh mentions in earlier flashbacks. This is also why it comes with a time out.
In addition, Katakuri's Kenbunshoku Haki (Observation Haki) is at a level where he is able to see some moments into the future. This is what made him next to impossible to defeat.
However, there are always conditions associated with such extreme powers. In Katakuri's case,
He needs to remain calm and collected for his haki to work. In addition, an opponent with mastery of the Kenbunshoku that matches his own would be able to counter him, since the future Katakuri sees can be altered by anybody. Source: Wiki
When Luffy fights Katakuri, he manages to trigger both these conditions. The first one happens when he interrupts Katakuri while he is eating donuts, though it does not last too long. After which Luffy gradually starts becoming better at using Kenbunshoku as the battle progresses, which prompts Katakuri to attempt to end the fight as soon as possible.
Apart from all of this, one must also recall that Luffy escapes in the middle of the fight using Brulee when his Gear Fourth runs out, and returns after his cooldown is complete. Katakuri could have easily knocked him out in this duration had he not escaped.
Thus, the results of the fight can be said to be more of a draw with Katakuri deciding to let Luffy be for now (since he considered him an equal by the end of the fight, and possibly realized that he would have to expend a lot of his power to deal with Luffy due to him never backing down), than a clear victory.
- First thing I wanna say is that, while katakuri caught having Donuts , it made him angry, he lost his chill and that wasn't the moment when Luffy started to see future.
- While Luffy was on a run for restoring Haki he had Brulee. So, there was no way for Katakuri to exit the mirror world and search for Luffy rather he used his brain as, if Luffy is running away, then he won't come back and started searching for another way around to exit the mirror world. But as the place Luffy entered to the real world and saw big mom, he traveled back to mirror world which ultimately enables Katakuri to find out his whereabouts.
- And as from the trick of Katakuri's younger sister (Flampee), Katakuri felt some shame as he started to enjoy the battle. So he attacked himself with the spear and then they both started with their all out. But as rubber guy and his will to protect (as a part of plot) luffy did not consider that Injury as major one but it felt right on mark to Katakuri as he never backed down or felt any of that.
After they both started all out, and then it's where the game began to shape out.
- List item At the end, it's just that if Flampee wasn't there interfering with battle then Katakur's had won easily. But after that katakuri got no chill and started getting Offensive instead of defensive.
Luffy won with Haki of Observation became strong. while Katakuri did not lose until Luffy promised to come back for a fight