One problem with health care in the U.S. is that prices are hidden from the customers. That interferes with a free market. Tax regulations incentivized tying health care to employment and Obamacare making it difficult to get catastrophic care both interfere with a free market, etc.
Another set of problems, as you describe, is the ability for private equity funds to collude and impeded free markets. Especially lobbyists getting laws passed in their favor, medical associations limiting the supply of doctors, doctors incentivized to prescribe opioids, etc.
The original post in this thread referred to our current health care system as a free market, and that is not accurate. That's probably just as wrong as saying that we currently have socialized medicine, and its not working.
I would say that our current health care system is a not a free market and is not socialized, it is broken mix of the two.
It won't be reformed any time soon because millions of insurance industry jobs would need to be eliminated to save any money. Good luck with that.
But that is precisely a market effect of PE being able to do this due to lack of effective regulation, isnt it?