I think what all of these countries have in common is that they have a strong entity negotiating prices on behalf of the patients, drastically lowering the price, and to a varying degrees also dictating what treatment is appropriate.
It'd be really nice if health care could work like a regular market, but evidence and intuition suggest it simply doesn't. As others have commented, people don't comparison shop even if they could. It's a bit like having no idea how a car works or what could be wrong with it, and then being asked to pick the best mechanic and strategy to fix it. Except of course, that it's not a car but your life or somebody else's depending on the right choice. I think it's unrealistic to expect a working market economy to develop under such circumstances.
One or multiple big entities negotiating prices and dictating treatment comes at the cost of less freedom for the providers and also less freedom for the consumers. Whether it gives better or worse care I wouldn't be too sure - on the one hand, special cases won't get specialised treatment, on the other hand trusting the decision of what needs to be done effectively to the provider sounds like it will cause over-treatment.
The freedom aspect probably drives the USA to the current system, but given the measurable effects, it just seems like bad policy.