If we really want to make the story deep, why not make it deep NINTENDO style.
Seriously, a Nintendo character breaking the rules for freedom to benefit everyone, while putting this very world at stake, really isn't Nintendo.
No, what's more likely is this.
What if those purple dudes are robots. I mean, real robots. More specifically, robots which not only resemble our favourite characters, but were made to replace these characters, to take their places in this world, Terminator style? To do that they need to capture every character and turn them into trophies. Of course, you can take each character's trophy back (e.g. save them), thus unlocking them for the story mode.
Think of it. What if breaking the rules means no more trophies to battle with? Our own world's rule is this. There are people who live, talk, breathe, eat, sleep. These are the rules of our world. But when something breaks this rule, something terrible would happen. What if that terrible thing means the disappearance of the world? According to some philosophers our world is created by us being here. Without something to percieve this world, this world would not exist.