And then a game gets updated so the hashes don't match and uh oh, everything is fucked. Oh, but we can change the hashes of the files in the executable! Yeah, so can they. People modding shit into the executable is basically a given. Let alone the fact that you'd need to sit through a steam "validation of files" length of time every time you'd need to launch a game (because validation works exactly as you have described).

What is gained is that it has access to more information. Some cheats use an entirely different program / process that reads memory and outputs info that is available to the game but hidden from the player. Like a client needs to know where a person on the other team is to be able to draw their model. So you read that, you put a little box over where they are, and bang you have wallhacks.