Here in Cyprus, healthcare works on 2.65% flat tax on all incomes, capped at 180K EUR income per year. Everyone seems happy and a family doctor makes 150K EUR per year, on par with the US earnings in a country which is much cheaper to live in.

Secret is much much much lower usage. People just use healthcare perhaps 10% as little as Americans do. It's just not in the culture. Life expectancy is still 83.5 years vs 79.0 in the USA. And yes we also have a car-based society with most people living in individual houses just like in the USA, almost no usable public transport, most of Cyprus is literally US-style suburbia, and in addition, everyone smokes.

So here is the advice of what to do with the healthcare: crush it. Same with universities, for the same reason. Many, many more people undergo unneeded medical interventions because of feeling compelled to do so for some cultural reasons, and many people also get useless degrees which they are unable to put to any good use, crazily jacking up prices for both healthcare and education.