With the game as it currently is, playing with 4 or 3 keys is hard, since pressing each button in a pair disables a corresponding key on the other pair.
If all buttons worked independently, there would be some patterns where using the extra buttons would be easier for most people. For example, managing to move 2 fingers fast enough to do a 300bpm stream is much harder than doing the same 300bpm stream with 4 fingers.
As such, allowing more independent keys would disrupt the way the game is currently played. Mapping 1/8 streams would be much more common, for example. pp calculations would need to be adjusted to take into account the easier to do faster streams. It is possible that overall players find the game more fun that way, though.