Dreams aside, in order to have a free market healthcare, which is what informed libertarians want, you need to abolish medical license, the FDA, patents and many other State's interventions. There is a reason why the healthcare system in the US is insane, and it's because the laws are made so that cronies have the monopoly on your health. Neocons are pathetic when they defend the current system.
Without the free market (the real one, not the scam you have in the US), healthcare will be a mess more than any other industry and at that point is better to have a single payer, universal system, because in the end they have the same problems of the current US system but at least you don't get ruined.
How can a market like this exist when the buyer is incapacitated, not to mention even when not incapacitated, the buyer is not sufficiently educated to understand what they are buying?
Also, supposedly people aren't total dicks. At the moment the healthcare industry rewards a lot of psychos due to its incentives. Hopefully with a free market the dicks would be weeded out due to increased choices. Also having a free market means that there would be an incentive to make medicine more accessible, while still correct, because more people could be willing to become healers, maybe specialized healers. Who knows, what's certain is that we have not discovered the full potential of humans healing other humans and the current regulations are a big brake on new systems and innovations.
So, for now I'm ok with the whole single-payer/universal healthcare deal.