It has already been done, e.g. windows DEP. Main blocker is that software which generates code needs to be adapted to tell the OS where it put that code.

Attackers adapted by e.g.inventing Return Oriented Programming(ROP): As they could not inject code into processes directly, they started overwriting the stack with adresses to interesting functions. When an attacked function returns, it does not resume the caller, but executes code in the executable chosen by attackers, with args dictated by the attacker.