I do like how Luffy is beginning to "bloom" his haki in this difficult fight to see the future as does Katakuri. I'm sure Luffy will show to notice it, and begin to harness it, and Katakuri likewise will start to worry and become flustered and angry at Luffy becoming more powerful.
It certainly seems that Katakuri could have mastered this haki at a very young age against someone incredibly strong, and since then has remained undefeated. If what Rayleigh stated is true, you cannot truly train such a great haki unless you encounter/fight someone stronger, then this must hold true for him. It would be nice to see a quick flashback of Katakuri's past as Luffy starts to punch the shit out of him. In that way, hopefully it can calm some fans that think this "power-up" is shitty.
The only people that will be butt hurt and call it ass pull are precious Katakuri fans, the folks in Real life Flambe's club. It has been shown several times in the manga that people can advance during fights to defeat the adversary.
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What i feel is Luffy not defeating completly Big Mom but a draw with Katakuri. I see Big Mom letting them leave after eating the cake and Sanji getting an enormous boost in his wanted bounty. A chef capable of knocking out an emperor?
Luffy could have run after he escaped the mirror world, he went back, because he wants to advance above Katakuri. Draw does not make him advance above Katakuri. If the fight ends this way, it's not even a draw, Katakuri and his fans will feel Luffy's life was spared. That is not acceptable for the future pirate king and someone that plans to take down Kaido.
It doesn't even make sense story-wise, Hey Kaido, am here to clobber you, says who? the guy that got his life spared by BM commander.