I'm not sure which country you're from, but many EU countries do have private health insurance. The Netherlands, for example, has a system of subsidized private insurance, and a mandate that everyone buy a policy.
(If Americans are thinking, "huh, that sounds like Obamacare / the ACA marketplace!" then you're right.)
Painting in such broad strokes, the German system also sounds like the ACA, but it's really not: the high level description really erases key differences.
In Germany there is nothing like bronze/silver/gold plans. All statutory health insurance covers what is required to be covered by regulations, with just a few bonus services, at the regulated tariff plus just a few percentage points of variation. So the 90% of people in Germany who have statutory health insurance [1] have essentially the same coverage. The tariff is a percentage of income (up to a cap), not a flat fee.
[1] not everyone is required to have statutory health insurance, for example employees above an income threshold and self-employed people
The Dutch system and the U.S. system are not comparable. Health insurance in the U.S. is a “free market” that the government dabbles in with a little policy here and there. Health insurance in The Netherlands is controlled by the government, it is heavily regulated.
Healthcare is "free" across Europe, including in The Netherlands. The choice of The Netherlands' to structure their system as mandatory insurance doesn't change the nature of it, it is free at the point of service with the mandatory insurance costs paid for by the government when someone is unable to pay themselves.
No matter your mental gymnastics that is not how those Americans imagine health care in Europe works. And just for your (and our confused American friends) information there are several countries in Europe where "a point of (healthcare) service" will send you a bill.
Which European countries have a healthcare system similar to the American system? A system that has "insurance" (e.g: The Netherlands, Germany) is no less "free" healthcare than a system without insurance (e.g: England) or a system that will "send you a bill" like France. "Free" healthcare means that the patient will never need to worry about the cost of their treatment because it is covered by the system (whether through taxation, reimbursement, insurance does not matter). How many people have been bankrupted by healthcare in Europe?
The European/"Socialist" solutions are never obvious to Americans.
It is like parliamentarianism, campaign financing regulations, gun control, multiple political parties, etc. Americans call these things "Socialism" and then freak out about them and refuse to see any good on them.
... and "Chat Control" and Digital ID and forcing digital currency and persistent digital surveillance and conceding your national sovereignty to a council that can pass binding laws without your consent and ....
Let's not pretend either system is perfect, or that the _underlying principles_ that both systems hold are the absolute correct way to organize a society.
Americans have be primed with _decades_ of rugged individualism and the idea that collective action is inherently weaker/flawed (just don't think about Social Security). It might have been reasonably true 100 years ago that everyone could pay for their own health care, but we're now in a world where the average person is perpetually on medications that are expensive to produce, and will demand increasingly expensive medical interventions throughout their life (heart health, cancer care, etc.). Combine that with AI probably wiping out a ton of industries/jobs - something has to change. I'm not going to pretend to have a solution, but I think it is disingenuous to suggest any EU nation has it figured out either and is obviously correct.
While Americans have been primed, it's still relatively new. If any of the new deal proposals were proposed today, everyone would lose their mind.
The dirty secret: half of what makes living in America tolerable comes from new deal policies. Everyone knows it, nobody will say it.
A similar thing goes for the ACA. Republicans hate it, but at the end of the day Americans don't want to be dropped from their insurance plans for having cancer or some genetic defect. Literally nobody wants that, only out-of-touch political talking heads want that.
That's not to say any of these policies are perfect, they all have flaws. But if you ask the American people what they want but carefully never name policy names, it becomes obvious everyone is on the same page.
Just a minor clarification: The Money freaks out, calls these things "Socialism" and then dumps billions on red-baiting campaigns and political donations to defend the (highly profitable) status quo. Most citizens would just like some healthcare.
(If Americans are thinking, "huh, that sounds like Obamacare / the ACA marketplace!" then you're right.)