I think you have a point about the public nature of these jobs. That said, I picked these 3 somewhat at random. And though teacher and firefighter salaries are very much set by state budgets in the US, doctor salaries are not. (They are, instead, mainly set by a complex interplay of state funds, insurance company profit margins, and hospital/practice competition for doctors.)
Take, for two other examples, commercial airline pilots ($75k-125k per year) or paramedics/EMTs ($36-50k per year), neither of whose salaries are set exclusively by state budgets.
Consider this note I just found in researching EMT salaries: "Private ambulance companies generally have the lowest rates of pay, but may be more likely to hire newer or less experienced employees. Many EMTs start with private companies to get their feet wet. Government agencies such as [...] state ambulance services generally pay the highest, but they’re more competitive to get into and may have higher education requirements."
The State and Federal Governments already provide health insurance for a majority of citizens, and we seem to be rapidly headed towards some version of "single payer" universal health insurance. I think we'll start to see much more political pressure applied to physician compensation in the future.
Take, for two other examples, commercial airline pilots ($75k-125k per year) or paramedics/EMTs ($36-50k per year), neither of whose salaries are set exclusively by state budgets.
Consider this note I just found in researching EMT salaries: "Private ambulance companies generally have the lowest rates of pay, but may be more likely to hire newer or less experienced employees. Many EMTs start with private companies to get their feet wet. Government agencies such as [...] state ambulance services generally pay the highest, but they’re more competitive to get into and may have higher education requirements."