Personally, I think it's a silly idea. Doctors are staff officers, like a chaplain or doctor would be in today's navies. They're not in the command line.
I didn't like it when TNG did it with Crusher and Troi for the same reason. Command isn't just a matter of rank.
Others mentioned Scotty taking over, and if he was unavailable, then Sulu steps in--as seen in a few episodes. McCoy's not trained in command, so he would not be suited for the job at all--even during a crisis.