Why would Flash Kick be awkward? It's still Charge Down -> Up+Kick. It's just Up isn't Jump. It's Up. For Up Normals and blocking high or whatever you gain from getting three cardinal directions open.
As for attack buttons, I would honestly be fine with three. Use more command normals, after all, you have three more directions to use to compensate. I would probably move Collarbone Breaker for Ryu to an Up Normal since it must be blocked high, as an example. Up+Forward+Punch = Overhead. It could even be a universal input for everyone, like how Down+HK is sweep now.
Yes, if Street Fighter did this, it would change, and possibly not for the better. The three strengths of most Specials matter in SF. But for a new game, perhaps someone getting an interesting license to play with? Maybe give it a shot, see what three attacks and a jump button can do.