This is a purely anecdotal posting, so do not expect any well-researched statistics or citations. But I think the experience, even without an abundance of hard numbers, is very telling.
I was in a developing country this week- not the worst on the planet, not the best- and needed sudden dental care. I lost a crown and it turned out that the tooth underneath it was severly deteriorated.
So I went to what I was told was one of the best denstists in the country.
"You will have to pay more than at other dentists" I was told, but as I was expecting a quality service, I anticipated a higher cost.
This is a country where some regulation exists, and indeed socialized medicine exists, but this doctor had elected out of the socialized program to practice on his own- it is more lucrative. He is still regulated, although there are issues of corruption and resources in that regard. His most effective regulation comes from his reputation, where he is known to the wealthy, the hotels, the embassies, etc. as acceptable.
I was in and out in about an hour and a half, and it appeared to me the work was as good as anyplace else (maybe a year from now I will need to rewrite this). Perhaps the best part was the cost. I actually made money in the transaction.
My crown, installed at great cost to my insurer several years ago, was made of gold. The dentist this week switched that out with an imported plastic type crown which he claims will do the job. I was given the gold crown back. It weighs about a tenth of an ounce. The work cost me about $80. So in the end, I made about $70 off of the visit.
Who says the free market does not provide decent, affordable medical care? You just need to leave the US to find it, I am afraid.
Sensible libertarian views on nearly everything- except foreign affairs.