> Can't the operating systems simply have an option when creating a process that prevents all operations looking at the memory of the process

Already the case for userspace programs, due to virtual memory

> those programs have to use OS facilities to mess with the game anyway.

Cheats today essentially are like drivers, they do not run as userspace programs. Hence, they can do literally anything on your computer. In terms of privileges, driver code runs at a level as privileged as the operating system. Hence the need for programs that run at the level of the OS kernel to catch the cheats.