Couldn’t the server just check what vision a player should have and not provide any other information to prevent wallhacks or maphacks?

Definitely not how that works. The server has no idea how to tell how the GPU on the client-side is rendering anything. The server is just doing server things, which definitely doesn’t include data on the “vision” of each player. There’s a lot less data being transferred than you assume here.

All of these are way easier to detect client-side, because client-side you can actually check the code that is running.

A server that checked all the code that is running would be a very, very slow game. Like imagine a chess game where it took five minutes for a move to register after making a move. Servers focus mostly on “player state” like, where are they, what direction are they looking, what direction are they moving, what buttons they are pressing, and a lot less on checking the code of the remote player. Once again, because checking literally every players code remotely would slow everything way the fuck down.