Be careful, that's inductive reasoning at best. We have exceedingly high health costs for a number of reasons including, but not limited to, the fact that we lead terribly greedy, indolent lives, the fact that we are gluttons, and the fact we insist upon using the extend the lives of a handful of people by a few (very miserable) months or a few (even more miserable) years at great cost.
Having said that, yes some form of price controls would no doubt alleviate the costs. It's a tricky business, though. The Price Theorist in me says that it will lead to shortages in services.
Analyses have regularly shown that something like 20-25% of our healthcare costs are just administrative costs above and beyond the average of what every other rich country pays. Our system has a lot to do with our costs.
Of course, the unhealthy lifestyle most Americans lead has to do with that too, which is a separate issue.
The Price Theorist in you is ultimately wrong. I suggest reading The Healing of America, a book in which the author travels the world to recieve treatment for a bum shoulder, seeing other countries' health-care systems from the inside. Throughout the world, governments put price controls on medical services and the people in those countries have easier access to healthcare than Americans do.
Doctors don't make as much money, insurance companies don't make as much money, the country spends less money on healthcare, and people get better treatment and more access. It's worldwide.
http://www.amazon.com/Healing-America-Global-Better-Cheaper/dp/1594202346