The last thing a medivac flight nurse/paramedic wants in the pilot's seat is a doctor. They want somebody who can fly the machine and work the radios at the same time, and who isn't going to kill them.
They wouldn't want a doctor sitting in the back interfering with their patient care either
Best place for the doctor is in the ER/Casualty dept to sort the patient out who has been brought there alive as quickly as possible.