If you compare it to card games like Hearhtstone, where people could potentially play a completely random deck of 30 cards (which never happens anyway), then changing like 3 moves per variation shouldn’t be that big of a deal. After some time there will be a meta with the same 2-3 (strongest) variations of each character anyway. Not much potential for chaos and randomness imo. (Easy to patch as well) Additional to that, there are already some limitations in the game for custom variants. Some moves can’t be used with certain other moves in the same variation. (Which would be another way to fix/patch things: If something is too broken, just make specific combinations „clash“ and therefore unusable.)
(And just to clear up my comparison: I think card games and fighting games have a lot in common, aside from the execution aspect. A lot of decision making, thinking 5 steps ahead, mind games, ressource management, tempo and so on)