I see a problem in the US system, the insurance companies have two options to make profit, (1) drain the insured people and (2) negotiale the the medical providers. This puts insurance companies in a very privileged position. This is why the insurance companies are the problem. Germany for example has a national "public" health insurance system and a private insurance system. The national health insurance system is based on an tax-based insurance font. For the public insurance sector this font is the only one (!) allowed source of income for the insurance companies. This means the companies can not drain the insured persons, they have to negotiate prices with the medical providers.

Switzerland does however have government set drug and procedure prices even if private insurance companies manage the billing. They are also one of the more expensive of the developed universal healthcare nations - though still significantly more efficient than the US system.

They are also very small countries compared to the US

Why do you think that's relevant?

In any case, the same point would apply in the other direction.