That's actually fairly common in fields where mistakes can be dangerous. Most places refer to it as apprenticeship, but it's fairly common in even less glamorous trades like electrical work, carpentry, etc.
The difference as far as I know, is that apprentices have normal working hours, while residents are sleep deprived to counterproductive levels and they could be barred from becoming a doctor at the end of it. If residents had normal hours like the rest of the doctors, I wouldn't nearly be nearly as apprehensive about it.
