Sure, you can treat I/O functions as World -> World functions, but unlike other pure functions, the compiler can't compute them at compile time when they are ap

Sure, you can treat I/O functions as World -> World functions, but unlike other pure functions, the compiler can't compute them at compile time when they are applied to constant inputs. A program consisting entirely of pure function applications to constants can be evaluated at compile-time to just the constant(s) it would output, while a program that calls I/O functions cannot be (assuming those calls to I/O functions are not dead code).