erm... Your first-order estimate is fine. Now look at the second-order equation:
What do people do when they are on a fixed salary? They look for extra income, especially when they have an inflated sense of self-importance. Whether doctors, politicians, or other government officials - they get bribed by whomever can benefit: namely drug manufacturers (doctors, dentists, health workers of all ilk), lobbyists and big businesses.
There's also the fixed salary but then putting doctors onto fixed schedules where they have to see 1 person every 15 minutes. Or 10. Or whatever the performance standards are nowadays for your health facility of choice (really the health 'provider' which is the insurance company, not the facility itself).
You cannot create a system which cannot be gamed.
This world continues its downward spiral into insanity.