Pokemon makes sense, its a game based off of turns where the outcome is for the most part predicted and stat based so a bottom tier Pokemon is just not going to beat a high tier Pokemon in a normal setting. With a fighting game however, it is possible to beat high tiers with low tiers if the player is significantly better or the match up says otherwise. As far as separating, I'd say no, but little side tournaments like low tier tournaments are fun on the side.
Besides, taking out characters change the tier lists because many fighting game lists are based off of how well their match ups are. Take out some characters and the tier list changes. And then you debate about who is supposed to be in A or B or C.
Edit: Oh and game is not that bad as far as balance and blah blah early blah blah blah :]
On a side note: they tried doing something like this in MvC3 on the side by giving each character points based on their rank and your team could not exceed a certain number of points. Was a really interesting idea at the moment. Your idea is interesting too, I just don't see it with this game as of right now.