Thinking about my limited knowledge of different countries health care, I suspect that the crucial thing isn’t whether a country’s health care is privately-funded or state funded. Nor, I suspect, is it crucial whether the hospitals themselves are run by the state or private business or the Martians.
I think the really vital thing is whether the politicians get the same care as the rest of us. Since they’ll take good care of themselves (obviously), that means they’ll take care of everybody else in the process.