Ok, I concede that it's feasible that state-owned and state-financed entities work well (my village is excellent at clearing snow from the road, which the municipality pay farmers to do). But I wouldn't put hospitals in that camp

That is laughable. The publicly funded British Health Service is massively more effective in providing universal healthcare than the US privatised system where many people have little or no cover. Public healthcare provision is one area where demonstrably state provision can be and is vastly more cost effective than the US privatised health system which is the least efficient most expensive least equitable in the developed world buy a large margin.