Suppose you want to remove the profit motive from healthcare.

If doctors would still get paid above-median wages, you would still have a profit motive. Their lobbyists would want to limit the supply of doctors or simply lobby to have the government pay them high wages, to require that things be done by a doctor instead of a nurse, etc. Likewise the drug companies would lobby for the government to pay them more for their drugs, and when the government is captured then that's what happens. The same problems we have now; you haven't solved anything.

If doctors would get paid a lower wage but still have to attend 8 years of medical school, there wouldn't be a profit motive, but then there would be a shortage of people willing to become doctors, patients would have to wait a long time to get an appointment as they do in places like France, etc.

The profit motive isn't the problem, that's the thing that causes anyone to want to (and be able to) provide healthcare. The problem is the corruption. You have to stop limiting the number of medical residency slots and allowing drug companies to patent trivial changes to preexisting things etc.