I'm not the biggest fan of French Bread games but I really like the beat edge system. It feels engaging enough to the players without requiring a careful balance of frame data to keep something from being totally overpowered by accident.
Anyways for my POC I was thinking of doing a 3 button game, ABC, with C being a system mechanics button, but it felt kinda underwhelming when doing the designs, as 2 buttons IS simple enough to prototype but doesn't really provide enough diversity to make beat edge interesting. So 4 buttons it is, ABCD. I wanted to add more moves but with only 2 buttons it felt annoying trying to cram so many command normals in.