Tradition, hazing, survivorship bias, and the fact that the people who are in charge of the system are only starting to think of quality-control statistics as something that could apply to the practice of general medicine.
My brother in law just finished a residency and we asked him the same question. Apparently more mistakes are made in hand offs between doctors than from tired doctors.
I am too lazy to check since I'm on my phone but I believe in the UK between less fatigue and fewer handoff errors it's a wash except for surgeons where there's a clear loss, as in under the new system more patients die.
There have been hospitals that have cut resident hours to more reasonable schedules. They measured the number of errors, hoping to see a drop. Unfortunately, the number of errors stayed the same.
The problem is that shorter hours increases the number of patient handoffs between doctors. Most residents cap at 12 patients. So, as you're trying to get out the door to go home, eat some food and sleep, you have to brief the incoming doctor on 10-12 hours of care for 12 patients. Either you have to go fast and skip some stuff, or you'll be there forever.
So, what's really needed is a better tracking, monitoring and handoff system? I don't know anything about hospitals, so have no idea how they currently do things and if there even is a way to make a better system work (and if they would even budget for such a system), but just going by the comments here, it sounds to me that there is a big need for improvement.
I think it's probably more about protocol. One example is that some departments would hand off in alphabetical order by patient name. Seems logical, but if Ms. Abraham is doing just fine, but Mr. Zimmerman is in critical condition, well, you can see the flaw. They found that doing handoffs in order of severity helped decrease error rates.
The other issue is interruptions. Hospitals are busy places, and sometimes someone needs to get in and get some information from one of the doctors doing the handoff, causing a legitimate interruption. As we know, even a few seconds can derail your whole train of thought. It's definitely still an open problem.