It doesn't matter what kind of debt it is, the only thing that matters is that the two have a history together that somehow allows them to reason with each other to a certain degree. The latest chapter proves this as BM called to give Kaidou the heads up that she's coming for Luffy and that she wants to keep this friendly. If this was anyone else, do you think she would have bothered with that? And the fact that Kaidou used as argument that it was a long time ago, indicates it wasn't that small of a debt.
And even if you ignore all of that, again BM is there to kill Luffy because he humiliated her. She being saved by Luffy would only make things far far worse, that's turning everything upside down. Also BM doesn't listen to anyone, that became quite clear from the WCI-arc.
For some reason your premise is that BM is there to take down Kaidou, is severely weaker than him and thus would lose, which would leave her no other option than to ally herself with Luffy, but that's not true. Luffy is the goal, Kaidou is nothing more than an obstacle to reach that goal. How does it make sense that she would use her goal to overcome the obstacle? To side with Luffy, she would have to talk with him and if she can do that, she can kill him. It immediately voids any reason to collaborate.
If your argument is Katakuri, well he isn't BM. BM is the captain, not him. The only scenario that this would ever work, would be when BM is not able to do anything and he decides on his own to ask Luffy for help, in which case this wouldn't be an alliance, but a submission and if BM would be given the chance, she would murder the hell out the both of them as the humiliation she would suffer, would be infinitely greater than the shame of WCI.