I think the high jump could’ve been handled by either holding the jump button down to control the height like most platformers do or by having a system to time the jump in a multi-jump sequence to gain height like Mario 64 used. I also don’t see why a double jump wouldn’t suffice as an unlock in its place.
This is a key example of what I mean by the nostalgia is holding them back. The moves are mostly copies of BK and it didn’t need to be that way.