You're taking this too seriously.
It's not really a story thing. They're usually just there as mythology gags and such.
If Smash had rivalries, I imagine they'd work like they do in Playstation All-Stars.
Eh. I don't like it in Playstation All-Stars (I don't actually know anything about it other than the fact that they have rivalries), but I like it even less in Smash. In PAS the characters are standalone while in this one a lot of the characters are coming with genuine rivals, it just feels weird to have some people crossing the universe gap and some not. Also, more importantly, in PAS some of the rivalries make next to no sense at
all, and if you have to stretch that far, what's the point in bringing attention to it?
Maybe in Bioshock you actually are killing Big Daddies as Sackboy the entire time and just don't realize it since it's an FPS.
Or maybe rivalries in a game like this just don't fit.
(and yes, I am taking it too seriously- Smashboards and all. It's serious business.
)