Theoretically, yes, but high-control characters would be able to complete any level a low-control character with the same physics could. For example, there's no elegant way to make predetermined jump arcs (like "Ghouls and Goblins") necessary, even though they can greatly enhance a game.
maybe a point system? high speed, high jump, high control, and double jump etc cost point, and you only have finite point... etc
btw im not a good puzzle maker, so im not making game lol, just talking
because even high control is already overpowered, i think everyone will add doublejump if it give you for free
and there will be some medal, cost medal need low cost, speedrun medal is fast enough, maybe.