Fwiw, a lot of European healthcare has both a public and private option. You may pick the private options because they are "better" in some ways (e.g. more modern clinics, shorter waiting times, or sometimes just better care) which still leaves some wealth gap, but usually means no one goes bankrupt to cure cancer.

The UK has both universal healthcare and private options that are far cheaper than the US.

Most universal healthcare systems coexist with private options paid separately. Some are provided by private healthcare providers, and then too tend to coexist with privately paid services.

It's silly to say "having options but you probably won't choose them" is the same as "no option".

There's probably a decent point nearby about subsidized (or tarriffed) work messing with the benefits of free market pressure but it isn't this silly overstatement.

> there would be no private option because nobody is going to choose to pay out of pocket in addition to their taxes that already pay for care

Every wealthy country besides Canada that provides public care is a counterpoint to this.

You realise that the impossible situation you describe is present in various places? Public and private healthcare systems existing in tandem.

You only rely on social security? No 401k for example?

Because that's the public option in retirement and you can have private options like 401k on top