But no one is disputing that.
The problem was that Katakuri has his pride and for him to defeat someone with the help of someone else, doesn't satisfy him.
I'm the same on online games, to put it more specifically, Battlefield 4 when i was one of the top Jet pilots. I hated it when some other jet would come in trying to help me, it just made it really difficult for the other guy and I would get no satisfaction in beating another good pilot with the help of someone else because it doesn't show my skill. Sure teamwork is required to defeat the opponent and its a teamplay game, but I take pride in beating people 1v1, no interference.
That's why I understand Katakuri's emotions very well.
Luffy on the other hand is different. Luffy in Doflamingo's case, has an objective, that objective was to stop Doflamingo from killing an entire country. He doesn't give a shit if his opponent is weaker and it's unfair, he needs to take him out to save his friends.
All I'm saying is that Katakuri willingly gave Luffy this victory on a silver platter.
Whether it's stupid or understandable for Katakuri to behave like that is irrelevant, Luffy won because Katakuri was "Honorable"