Maybe I'm looking at it differently. Straggler said the cost of US healthcare was unjustifiably expensive. I was considering the total cost of healthcare in general and thinking that we do a lot of stuff at our hospitals that can drive that cost up (research, etc.). That's going to lead to an increase in cost to the individuals who are paying into it.
Even although medical research may sometimes be performed in hospitals, that does not mean it is part of the normal hospital budget. Funding is normally distributed by national institutes like your National Institute of Health, and only 31% comes from government, the rest coming from the private sector. Also the amount of research is 2.68% of GDP (compared with 1.88% of GDP in the UK) but as far as I can tell this is not included in the 16% of GDP spent on health care. All these fun statistics and more can be found on wikipaedia
here and
here.
All governments need to spend taxes on the basic infrastructure of a health service i.e. facilities, staff and equipment. However in countries with universal healthcare we also fund everything else, such as the costs of performing procedures, drugs, after treatment care etc. Now as far as I understand your system all these additional costs are covered by your insurance companies. So a large part of the costs universal health care systems have to deal with should not be required under your system. So the question isn't why does US health care cost so much more, it's why isn't so much less than a universal care system? Just where are those insurance premiums going?