Take a group of hospitals, randomly assign them to "continue insane hours for residents", "40-hour work-weeks and no more than 12-hour shifts" and maybe a third group somewhere in between. Run it for two years, and see what the effect on patients and doctors actually is.
Then will come the hard questions: if we see that these insane hours are literally killing patients, surely then it will make sense to end this madness?
Yes, long shifts kill patients. But the other thing that kills patients are handovers -- one doctor forgetting to note or tell another doctor a crucial detail at shift change. Longer shifts mean fewer shift changes.
However I don't think the additional staffing costs will fly, you're talking a hugely substantial increase if you were to enforce this - more than 25%, since current staffing levels are so thin.
It's a balance of what people are willing to pay, the risk we're willing to accept, how ethically we treat workers (doctors). Unfortunately, like many places in the economy, there aren't rational actors on each side to negotiate these things.
The major issue (other than $$$) is thought to be hand-offs: information gets lost when one caregiver takes over for another. For example, you might notice that Mrs. Jones looks just a little bit paler than she did earlier, and take that into account when treating her, even subconsciously. This gets lost when a new doctor takes over, and allegedly, the increase in hand-off-related issues is not outweighed by the decrease in sleep-related ones. That said, I'm also not convinced that this has been aggressively optimised, or even tested over long-enough durations that people adapt to increased hand-off frequencies.
http://www.nejm.org/doi/full/10.1056/NEJMoa1515724
One of the main challenges of course in this area is looking at patient outcomes with an incredible amount of potentially confounding variables, since "resident work hours" is just one of the many things that influence patient outcomes at a hospital.
This is probably the best that can be done without totally reworking the hospital, but it's not exactly a sensible test: data from lab experiments shows performance cratering well before that.