Why is anti-cheat always client-side? - eviltoast

Why is it not more common to implement anti-cheat on the server instead of the client? Is that not more secure? Couldn’t the server just check what vision a player should have and not provide any other information to prevent wallhacks or maphacks? Or check how fast it is possible to move to prevent speedhacks? Aimbot is a bit harder to detect I guess but what about the other ones?