What stops you from tampering with the game folder, and changing the function that sends the hash, to send a pre-calculated and valid value, instead of calculating it from real files you are running?

So save files exist. Also custom user content. So the hash will change accordingly. Plus some cheats don't require a modification of game files anyway, they use memory analysis to get, say, the location of other player objects, then they manipulate local information to give the player an advantage. This is how aim hacks and wall hacks work.

Cheats are hard to prevent for the sole reason of you don't own the computer they could be running on. You can't trust the user or the machine, and have to design accordingly. This leads many to the "solution" that is kernel level anticheat, it gives total access to the system.

Games probably do this in some way already with something like a checksum but the problem is you could have some separate program reading from game state/display at runtime to get around this. That's part of why a lot of cheats are installed at a kernel-level.