It's peculiar that medical residents are systematically sleep deprived but commercial airline pilots cannot fly/work longer than ~8. Most of the time the plane is on auto-pilot, but there's no such thing for zombie residents doing triage at the ER.
We are expecting new duty regulations later this year in response to scientific data on fatigue and the crash of Colgan 3407. Currently the data shows that on a four-day trip we are equivalently drunk with fatigue by the afternoon of day three even with around eight hours of sleep. Most people really need about nine.
Personally, I've never intentionally flown fatigued but I have been surprised by it. By the time I notice I'm fatigued the heading indicator looks like alphanumeric soup and I cannot differentiate 030 from 300 from 330 without the utmost concentration. I tell myself to "THINK, DAMN IT", but that is futile. It is something that cannot be overcome.
Having this experience, there is no way I'd want medical attention from fatigued doctors. Sleep is important for any safety sensitive job. It's always better to error on the side of safety.