It didn't work, not because of technical issues, but because we didn't anticipate the high number of doctors that apparently had lost their badges and had never faced consequences for it (the culture at this hospital was "oh you forgot your badge? no worries, I'll just open the door for you"). When we then asked the medical staff to keep better track of their badges (not just for the login system but also because of general campus security) we received incredible pushback, and that's when we had to roll back the program.
IME, and as evidenced by the VA using a similar system as you mentioned, doctors are perfectly competent enough and able to use these systems and do just fine once they get used to the system. The issue is that they put up a fight more than anyone else when introducing something new, and oftentimes IME the new system never gets a chance before it's shot down.
Security IT is, in my experience, one of the most amenable in terms of trying to come up with new ways to serve customers because the customers require it (all customers require it, not just doctors), but doctors are on an entirely different level when it comes to resistance to change.