Health care is a situation where competition cannot be a spur to reasonable costs because individual consumers are simply not in the position to make the kind of "free market" choices that economists (or more often free market ideologues) expect they'll make.
Moreover, the malignant and abusive US health care system is in fact a product of layer upon layer of failed "efforts to create competition" intended to reduce cost "through competition" to the point that by now all the abusers really know the dance and will be profiting next year from any further or replacement layer you add this year. (and "no regulation then!" as the US 1900 results in doctors being just heroin dealers - like my great grand father interestingly enough).
Most other industrialized nations have a state run medical system that's far superior and cheaper than the US system. They didn't solve their problem with "competition".