“I think that it’d be more interesting if you could still do things as normal regardless of how long you’ve been awake, but got progressively greater penalties to every action according to how long it has been since you last slept.”
That’s pretty close to exactly the way it is now. You can go two or three days without sleep before dying of sleep deprivation and your skills start to get pretty severely penalized after about 24-36 hours of not sleeping.