My issue is less with what we call the individual markets in the experiment. It's more with looking at healthcare across a large data set of countries and finding a general trend that more regulations lead to better cost structures and better health outcomes for the population and then somehow jumping to the conclusion we need no regulation for everything to work. That's just inconsistent with empirical reality and it's one of these purely ideological fantasy-land claims.
I would very much like to see a study from a credible source who came to this conclusion based on a survey of different health care systems.
What I believe is more likely is people looking at the kind of regulations being used and concluding that the correlation between good and bad regulations can be directly tied to the profit motives behind said regulations. A purely state run health care system has zero incentive to impose regulations that seek to raise costs and hurt competitors because, by definition, there is no completion. A purely private health care system has a lot of incentive to regulate the amount of doctors (to keep wages high) or make reporting costs extremely high to push out the smaller hospitals and increase their market share &etc.
I suspect that reality falls somewhere in the middle no matter what system you look at and everyone wants to argue from the extremes (or accuse someone else as being an extremist as you so helpfully demonstrated) so there is no real dialog for trying to fix anything.