The majority of the world still has, to my knowledge, for-profit health care: Britain, Germany, France, Switzerland , Sweden and Italy all have at least some form of private health care.
The United States definitely have a problem with health care prices. It doesn't appear from where I sit to be an issue with individual bad actors (although of course they do exist) but rather structural. In part, the well-intended federal and state attempts to improve things have backfired — as they tend to do — and made things even more expensive (which reminds me of federal student loans, another instance of well-meaning attempts to help the lesser-off which somehow seem to benefit the upper middle classes most of all; cf. also federally-subsidised mortgages).