Out here in the real world, in a country that has had socialised medicine for about fifty years, the only doctors that have ever been “forced to work for the government” were military conscripts back before they abolished the draft.
Doctors can charge whatever they like; the government refunds a set amount per procedure. If the doc charges the scheduled rate, the patient pays nothing and the government pays the doctor. If the doc wants to charge more, the patient pays up front then gets a partial refund from the government.
Doctors who charge dramatically more than the scheduled rate have many fewer potential patients, but some of them still do so, relying on prestige and quality of care to make up the competitive disadvantage.
Ain’t it wonderful to see market forces at work?