Speaking as a flight instructor, the problem with doctors and lawyers in the pilot seats is: They believe they are smarter then everyone and know more about everything and refuse to listen and learn. They have far to much money, which allows them to purchase advanced aircraft that are far beyond their ability to fly. Just look back over the FAA aviation accident reports, See how many low time pilots flying advanced, high powered aircraft and have dented the earth have an MD or Esq after their name.
This isn't a problem in the UK where doctors are not very smart. We know this true because our government tells us when it's looking for a scapegoat for the problems in the NHS.
Also we earn a fraction of the income US doctors enjoy. I know a lot of doctors and none of them own "advanced, high powered aircraft". If and when I get my ppl I'd be more than happy with an old PA 28 or 172, fairly decent ones can be bought for the price of a modest family car.
As for all doctors refusing to listen and learn, they'd never get through med school if that was true. Bit of a generalisation I reckon.
I agree with everything you said about lawyers though.