I think that empirical evidence is against you on this one. The US has one of the highest spendings on healthcare per capita in the world, while average life expectancy (one of the measures of a good health care system) is on par with Cuba. US yearly expenditure on healthcare per person is $4.500. In Cuba it's $100.
The American freemarket system clearly doesn't work very well.
The graphs alone should open the eyes of any who defends the current US system.
Of course Cuba and the US are both outliers. But realistically the US should be able to get results that are much closer to other first world countries.
While spending per person in dollars may be higher, there is gross gross inflation in the health care sector, resulting in the hospital charging you $100 for a pack of Kleenex, because it's usually the insurance company that pays it.
The American freemarket system clearly doesn't work very well.
Source: http://ucatlas.ucsc.edu/spend.php*