It would be cool, but what think would be better is having a "Create a variation" mode. Get a character with no specials and choose 4/5/6 (depending on the character) of their moves from the whole list of specials of the character, regular or variation specific.
You may even tie it with a reward sistem, so you have to unlock some of the stronger moves, or unlock slots to have more specials at the sake time. Maybe even get to have every move, but doing it over time.
I dont know, maybe it sounds lame, but I would pay for a mode like this, would love to see what people come up with.
Edit:
I have it all figured out, it should be like a card game or something. You start with 0 specials, by playing this mode online you get random (specials) from any character of the cast, by winning you get points and experience (the second being character specific). When you get enough experience you level up and get to add a card slot to your character, so thehigher level he is in, the more specials he/she can have. Points would be spent to buy the enhanced normals (IE: outlaw's/piercing's NJ, cryo uppercut etc. ) and variation specific strings.
Am I overthinking this? Have I gone to far? I dont care, I think it would be amazing. Dam, now I want it so much!