Here is an interesting discussion on the pros and cons of free market delivery of healthcare from a consulting firm in the UK. It doesn't seem to matter what kind of system you have, someone will always be complaining about it.
A market solution might be efficient, but I don't think it would be equitable. Our system is a mess. Whether it's more of a mess than the NHS in the UK depends on where you sit. Bottom line: we spend a lot more per capita than anywhere else in the world and have 47 million uninsured.
Quoting from the article:
"Within most societies there exists, in some form or another, a concern that health care resources and benefits should be distributed in some fair or just way"
From where I sit, this should be the starting point for any discussion. If you don't agree with this premise, what do you offer as an alternative starting point other than: It's all about me?