Perhaps I've misunderstood you here but in my opinion the way healthcare works is sort of the opposite of a free market and if a free marketplace for health services were allowed to exist then things like $500 bags of saline solution wouldn't exist.
- The U.S. is some sort of ungodly hybrid system, a muddling of free market and tightly regulated ideas, and has very bad outcomes for the amount of money we spent.
- Everyone else has gone away from a market system, more toward a regulated system, and experienced better outcomes.
It's possible that also walking away from the other end of the market and relying on the invisible hand to administer your IV will work, but it's not a notion supported by much data - it's a free marketeer leap of faith, and it's in an industry where many of the assumptions needed for a free market (information symmetry comes to mind immediately) don't exist.
However, the substantial majority of healthcare services provisioned are non-emergency.
It is absolutely possible for us to have a freer market in those services (Lasik procedures are just one frequently cited example) and IMO that would be a huge improvement over the current Frankenstein system we have today.