The pitcher still needs a target though, plus someone to call the pitches. The latter I suppose could be replaced by an ear piece or the pitcher throwing whatever they want but that sounds pretty f***ing stupid lol. It's really hard to aim at nothing, so I don't think the catcher's position would change at all, the catchers could just put themselves in a much more comfortable position like sitting up by their knees rather than a straight crouch. They still have to catch the ball when someone's on base and when a hitter has 3 balls or 2 strikes with no one on, so I don't think this is something fundamental to consider or anything.
Also the ball still has to get back to the pitcher, and it's much faster if the catcher is receiving and tossing back in their current state than sitting behind the backstop or something dumn like that. Foul balls are also a thing, that's why catchers are assigned to their circle and can't just stand wherever they want.