Alternate win conditions in a fighting game are super hard to design effectively. You could do unique abilities that are really cool like Naoto's Mudoon instant kill, but then there's balancing issues with how viable you want it vs winning a game with damage. And if you make characters with alts that are too strong, it upsets the pace of the game. You could make the game take longer on average to make alts that need setup more reasonable, but then the balance among the characters that win normally gets really hard to deal with. If you slow the game down to take 5 combos on average to kill instead of 3, the little differences in damage or mixups suddenly become a lot larger.
The other option is universal alternate win conditions like ring outs and stage hazards, but the problem there is finding a condition that doesn't seem random or frustrating to new players, or takes skill without becoming too complex.
As a thought experiment, I once tried to redesign a Kenshiro from Fist of the North Star based on alternate win conditions,and it was a real challenge trying to come up with solutions that are interesting to play with while not being frustrating to play against. There's a real risk of a player feeling cheated rather than outplayed by alternate win conditions. You really have to make sure what's going on is obvious and built up.
It's entirely possible that the best alternate conditions are the ones that still fit within the regular rules of the game, like the two Phoenixes in Ultimate Marvel vs. Capcom 3.
I don't know who that is.