Most doctors are not very rich at all, upper middle class. I make more than many doctors I know as a software engineer, and this doesn't even take into account their debt.
Care is expensive because of insurance. Hospitals needs hundreds of administrators and billing specialists. Very little of that money goes to the doctor.
Doctors deserve to be rich. They do incredibly specialized work where the outcomes are extremely critical, to put it mildly. I don't want doctors performing unnecessary treatments to line their pockets, but I don't think we're actually in danger of that.
The difference between a rich doctor and a rich insurance exec is that the doctor helps people, and the insurance exec makes their money withholding necessary care from people, in effect torturing and killing them.
This is the problem with insurance in general. The incentive of insurance is at direct odds with patients and doctors.
It's a tug of war, and even if insurance "loses", it doesn't matter, because you lost trillions of dollars in that tug of war. It's artificial inefficiency caused by privatization, very much a Dark Night burning a mountain of money situation.
Care is expensive because of insurance. Hospitals needs hundreds of administrators and billing specialists. Very little of that money goes to the doctor.