You keep saying that reducing call time is the "win." It seems like that the only metric you're measuring. If so, your product is a failure, not a success.
This is HEALTHCARE. You don't get to do "rough around the edges." You don't get to dismiss edge cases.
I also work in healthcare tech. My company doesn't permit such things because people die. I'll write it again because it's a point that tech fetishes can't get into their heads:
People die.