In fact there is no functional healthcare system on the planet which operates on a free market model. What is so fucked up about the US healthcare system is how little regulation exists regarding costs - wild variation from system to system and hospital to hospital and provider to provider; antitrust exemption for healthcare conglomerates (outrageous!); no ability for the government to negotiate drug prices with Big Pharma, as occurs in all the nations with universal nationalized healthcare.
This is one model where capitalism fails and will ALWAYS fail.
Single payer NOW.
Your statement is a non sequitur, implying that there is no free market system because it doesn't work. Despite there being many other variables, one of them being the simple fact that some people want to surrender their choice to people who want to control. This is a common theme in human nature, and usually leads to bad things.
Those calling for single payer want to leave the healthcare needs of the minority in the healthcare system in the dust, whether they realize it or not. Most don't, because they're too busy wanting to surrender choice to those they've accepted (wrongfully) know better. Some (e.g. Rahm Emanuel) does realize this, and is one of those who think they know better, and he is one who talks about those of non productive ages should not expect as much healthcare, since they haven't yet, or are no longer putting value back into society. Therefore they should expect less back.