As conditions diminish for health care workers, fewer highly qualified people will elect to enter a government controlled workforce. Longer hours and deployments to fringe areas will compel ever more people to avoid health care employment. Until one day, nobody want to become a doctor.
And then, what of the peoples' right to health care? Will the government have to start selecting youngsters with the capacity to learn medicine and track them into lifetime servitude as government physicians? I don't see how thay can avoid it.
Sounds like the later Roman Empire, when most occupations were hereditary.