When I go to hospital, on the assumption I'm conscious, the last thing on my mind is deciding which doctor I want

For ER agreed. For anything else that is serious / non trivial, you also want to consider the repuation of the department. Some doctors are world specialist of something, or treat dozens of a particular condition every year. Others rarely do or are simply not good. I don't think there is any way for a layman to know. You kind of need to ask relatives in the profession, who can themselves ask around. I have a few doctors as relatives and they systematically check the reputation.

> Can you refuse treatment from an OON provider in a hospital?

In most cases you will not know that it's an OON provider. You may be under sedation at the time.

The practice is outlawed in many states, as far as I know.