Switzerland [1]. And the Netherlands has a mostly-private system [2].
[1] https://en.m.wikipedia.org/wiki/Healthcare_in_Switzerland
[2] https://en.m.wikipedia.org/wiki/Healthcare_in_the_Netherland...
On the other hand, the state (each canton) pours large amounts of money into hospitals and research. There are laws and regulations at various levels (edit: eg how many doctors may open a new cabinet), and in these days we are reminded that doctors can be mandated to work when a crisis requires it.
Calling this a "completely private healthcare system" is a bit misleading.
The assets are privately owned. That’s completely private.
It’s not laissez faire. But those are different things. Subsidies and buying mandates are compatible with total privatisation, something often lost in this debate.
> The insured person pays the insurance premium for the basic plan up to 8% of their personal income.
So some huge portion is state-subsidized for lower incomes.
Medicare advantage in the US has similar privitisation aspects as well.