"Entirely productive" - but would you look at the mistake rate for the first two hours on-shift versus the last two hours on-shift?
If you do, don't tell anybody. They'd probably quit.
The collective ego and conscience of the medical profession, the way we treat them, tells them they should be unfallable, and mistakes are not only unforgiveable, but actionable. Medical residents should need no sleep whatsoever, should have no downtime et cetera, et cetera.
If we gave them a sane number of hours per shift (by the standards of the rest of the economy) and a reasonable margin to communicate patient status from shift to shift (rounds twice or thrice a day), we would increase labor requirements by 25%. If we gave them a sane number of hours per week, we would increase labor requirements by another 100%.
Work standards initiatives that have been successful include "Towards an 80 hour workweek" (down from 90+):
http://en.wikipedia.org/wiki/Medical_resident_work_hours#Tow...
Do you want your heart surgeon to have worked 80 hours in the last week, and 24 hours in the last day? Myself, I wouldn't want my doctor using the same public road network as I do, in such conditions.
How many people has this policy killed?