[Uberphallus]

A big chunk of European systems are neither of those three, there are three axes, one is regulation, another the practice, and the final one is funding.

France for example, has mostly public funding, relatively heavy regulation (prices are fixed), but practice remains mostly private (though mixed in hospitals).

Switzerland has mostly private funding, even heavier regulation (insurance is mandatory and you can't be refused for pre-existing conditions, for example), and most practice is private (some public hospitals).

The big elephant in the room in US healthcare is that funding is 50/50, yet you can only benefit from the public part by being old or extremely poor.