Oblivion did it with a 'fatigue' bar, pretty much the same thing as move. However, when the bar wen't down all the way it didn't stop you from moving, it just slowed down your movement. This stat had all kind of affects because it represented you being tired. It was more than an on/off movement kill switch, it represented the quality of your moves and your actions in general. That's way more complicated than CF's, but it is far more realistic.

In CF this would be something like:
100%-40% - all movement is normal
40%-10% - a varying degree of lag to walking
10% - impossible to go below 10% without some kind of malediction

This would give you a serious strategic advantage to staying refreshed as it is now. But, you would never need to sleep for moves, you just won't be able to run away when fatigued.