Why can't we have doctors that other countries have agreed are qualified to be doctors?
Also, do you know how certificate of need laws work? It literally says you can't have a hospital unless the other nearby hospitals agree you can have it.
Taxi medallions are truly a "there can only be X many people doing this" system, but even if they're not written that way, these other laws are still intended to restrict the supply of healthcare.
nb my issue isn't whether the healthcare system is "socialist" or not, it's that it's bad. I don't think "just make the government pay for everything" is a solution to things costing too much though; if an ambulance ride costs $9000 the solution is to make it not cost that, not to share paying for it.