Every country has for-profit elements in their healthcare system. The USA is uniquely dysfunctional in its governance. There is regulatory capture at every level.
You’re right. The Swiss system is deeply privatized, down to compulsory private insurance [1]. It just isn’t as opaque and corrupt as the American one.
Part of the problem with the American system is everyone is cynical with respect to reform, and has a singular bogeyman they’re convinced explains all of the problem, with zero room for multiple causation.
Not sure about that. But each person tends to have something like a single sentinel flag. E.g.: does medicare negotiate drug prices? And if there's a change for the better, they won't believe it's anything but a short term grift until they read it back as "true" from at least 16 different threads over the course of, say, 9 consecutive years.
Given that their representatives currently use phrases like "medicare advantage" to mean "off traditional medicare and on private insurance," that caution seems warranted.
It's not caution. It's reductiveness that contributes to the problem.
You might want to check that. In Cuba's case, not really unless you focus on their export of medical services. But for the greater case it's totally free. And qualitatively better than what the US provides.