I think it'd be a lot easier (and more satisfying) to ramp up firings than to put up an artificial cap. Honestly, you could ramp them up pretty far without being unrealistic. You take a crap program and build them into a perennial NT team, but after six or seven straight tournament berths, you still can't make the second round? Sorry, you're toast. (see also: Glen Mason Territory).
Now you don't have to get this extreme with firings, but you could and still be realistic, and it would keep a lot more jobs opening up. Of course, you'd have to change the hiring logic to make sure these new jobs didn't go unfilled.