It really isn't.
You are imagining cheats must be superhuman, rather than merely better than the player making use of them. It's perfectly possible to create a cheat which doesn't move the mouse impossibly-fast or impossibly-accurately; it just moves it as quickly and accurately as a top-1% player. The bottom-10% player doesn't care that he can't beat the world champion, because he can still pwn some noobs.
You are ignoring cheats which display extra information on the screen, which the server can never tell. Did the player shoot someone too soon as they came around the corner, or did they just react quickly? Or did someone on their team warn them? The server doesn't know.