We can start by asking if capitalism is inferior at providing health care, at least. People sometimes assume that capitalism means free markets. In practice it can also mean oligopolies, monopolies, rigged systems, and scams. That may describe the US health system, propped up with government regulations and subsidies.
For my part, I don't see a need to try out a more capitalist health care system when there are lots of people showing a good working socialized model in lots of other countries.
"In practice it can also mean oligopolies, monopolies, rigged systems, and scams" - Pure capitalism has none of those things. What you are referring to is cronyism which increases proportionally to the size of the market. Regulation should in theory be used to keep markets of sufficient size in check but it's a double edged sword. Often times regulation creates even more cronyism since only the approved players can access a communal resource or service.
Pure capitalism, the real world system dominant in the industrialized West in the 19th Century for which critics coined the term "capitalism", has all of those things.
The unrealistic fantasy later capitalists developed as a propaganda to sell capitalism doesn't have those features, but then it also has nothing to do with anything that is, has, or ever could be, realized in the real world.
The only unrealistic expectation is thinking people will be happy working unequally hard for equal pay. Capitalism funnels that motivation to set oneself apart into a system where many can benefit from the creations of a relative few. Politics came about long before the first political system. It stems from the evolutionary compulsion to compete and reproduce. There will always be in-crowds and out-crowds of any group of sufficient size. This is where cronyism comes from. Not the political systems themselves. Humans play favorites, not free markets
