I've had that theory Long ago.
If you take a closer look at WCI, it seemes pretty nice so far, you have a lot of Food, you havea peacefull own world, you have regulary parties.... The only Problem, unpeacefulpart is Big mum. For the whole Country, if theire would be a force more or less equal to BM to Keep that area safe, it could be kind of a paradise.
Also, Big mum is a burden for her whole Family, she is always threatening to them and can kill them just because she gets hungry. And i guess, when Big Mum for example would go for Brulee, Katakuri would try to safe his sister and in worst case, go against his mother.
He also could come to the conclusion to take his Family, Brothers and sisters, and even the citizens, out of the burden of his mother, when he can build a force strong enough to Keep them safe. And building an Alliance with Luffy, which gets already called Yonkou and which is still growing fast (Katakuri saw and mentioned exactly that he is growing extremely fast) could be exactly that force. If he is able to get into an alliance with luffy, from who he knows he is trustworthy in These matters (just Needs to take a look at Sanji), he has a force to stand against his mother and to Keep WCI safe, even without her.
And to declare this peace, to build this alliance, he could bring along Jimbei, as gesture.