You won't be able to replace doctors, because you want someone to say "I'm a doctor and you need this surgery". What will happen is the doctor will get an AI to help him, and then he will rubber stamp the diagnosis. He captures the gains.
Pilots and captains are also one of these. Someone's gotta be responsible for the people on board, even if a computer is already doing everything on a normal day.
Military planes have been way beyond unassisted human control for a long time now. I see no reason why airliners won't go down the same road (you can literally see it happening as we speak).
It turns out that dynamic instability has some real advantages (e.g., maneuverability), if you have a computer to help keep the thing from going out of control.
The AI may fly the plane, but the trigger is squeezed by a human.
However when AI does a job better people will be fine with AI taking on the role. We are fine with computer controlled subway lines, dishwashers, and some even driverless cars. We are happy let machines do tasks if we're confident they will do them well.