John, I think it has already been explained to you that that is PRECISELY what happened to private practice when the National Helath Service was set up in the UK after World War 2.

There was initially considerable resistance, much as you have dwelt on

"Despite Bevan's repeated guarantees of clinical autonomy for both family doctors and specialists, and a massive majority in favour of the NHS Act in parliament, the BMA chose defence of "clinical freedom" as its rallying cry for opposition to the new service. One BMA leader described the NHS as "a step toward Nazism as practised in Hitler's Germany". Only four months before the NHS was due to start in 1948, the BMA was still refusing even to negotiate with the Minister, a stand endorsed by 9 out of 10 GPs on an 84% vote."

However.......

"Two months after the appointed day, 93% of the population was enrolled, reaching 97% by the end of the year. In spite of themselves, the doctors' feet were indeed set on a new path entirely. They learned from their own experience that release from fee- earning improved rather than impaired doctor-patient relationships. Public service enabled them to serve more people more effectively, at lower cost to the nation, with greater personal security and integrity than they ever had in private practice. By the end of the 1960s, most were supporting the NHS as vigorously as they had once opposed it, and so they have remained."

from ORIGINS OF THE NATIONAL HEALTH SERVICE

I think many other people from the UK have also commented on the excellent remuneration that General Practioners receive for this service.