Hmm, and yet the US is not the only example of a capitalist nation with a health care system. The problem has more to do with regulatory capture. You can say that this is a consequence of capitalism, but then how do you explain other capitalist nations which do not have similar issues with their healthcare systems? There must be some aspect which is specific to the US, and personally I think it traces back to the degradation of antitrust enforcement under the Reagan administration, which allowed massive conglomerates to form.
Blaming this specifically on capitalism is too narrow, it ignores the broader sociocultural issues that lead to the current situation. Capitalism as it is realized in the US is more a symptom of underlying issues than it is the core of the problem. Attempting to replace capitalism with a different economic system will not resolve the problem.