In my armchair politics I do wonder if single payer, market provider might work. You get the competition of the market, but the tax payer purse. I think technically this is how medicare works but there are a bunch of nuances that make medicare not work (such as negotiation of prices).
I'm not sure if it's matches "single payer".
It has mandatory insurance. And you cannot choose most of the things that what you can get covered or not.
I got a "government insurance", which is the most expensive, but also the one with the best cover. There is "private insurances" with cheaper premiums and less cover that are attractive to young people, but it's kind of hard to later in life switch back to the government one.
Most countries in EU have kind of this mixed healthcare, with private, and public ones with the only goal to make sure the private offer competitive enough services... Same thing with hospitals, there is public hospitals, so private ones don't jack up the prices to crazy values...
I see, the American strategy seems to be increase competition to ensure prices are fair. A big problem being the corruption in the government through lobbying having a positive EROI such that companies are blocking good anti-trust policies (such as requiring transparency on prices) .
A lot of people are negative about how America does things, but as far as I can tell most of the issues stem from corruption via money in politics. Capitalism and Market Economies seem to work well, but Crony Capitalism and Citizens United seem to just be friendly names for corruption.
If either of those are true, their lives do not depend on those procedures.