Free market principles fail for healthcare for reasons entirely unrelated to those things, as has been pointed out up-thread. You're advocating for regulations to be eliminated as if that would fix unrelated problems. Do you care if healthcare is improved, or do you just want to see free-market-style reforms for their own sake?
In 2013, 64% of health spending was paid for by the government [0]. The non-profit hospitals share of total hospital capacity has remained relatively stable (about 70%) for decades [0]. The regulation section of Wikipedia is a litany of anti-free-market policies [0].
You can argue that free market principles fail in healthcare, and I will happily disagree and we can all have a cheerful time. But the US hasn't tried a free market approach to healthcare in at least decades. The free marketeers lost the argument; all the dials were set to non-free market and people argued that the quality/access to healthcare would rise to offset the cost of regulation. I'm not totally sure why people keep buying that argument.
In a free market:
1) Employment status would be irrelevant to healthcare.
2) People would be legally allowed to provide healthcare as long as treatment met whatever minimum quality standards the government sets on healthcare.
Saying "it became illegal to open a hospital" is unrelated to high costs is a serious failure of imagination. A ban on allowing people to provide competing services is a serious concern.
Also, people arguing for socialised healthcare aren't arguing to bring down the absurd costs, they are mostly arguing that the absurd costs should be shouldered by the middle & upper classes instead of the people consuming healthcare. It is unfair to first being in policies that inflate the costs, then dump the costs on taxpayers. If the argument is dump the costs on someone else then a decent effort should be made to reduce those costs.
People arguing for socialized medicine are arguing for bringing down the absurd costs, by virtue of having a very strong negotiating position and economies of scale.
Canada's single payer system is an example of that.
In a free market, employment status would still be related to your healthcare, eg. through credit checks to see if you're moral enough to get surgery. Theres no reason companies would stop providing healthcare coverage, and for providers to bump costs to match the extra spending power
> a very strong negotiating position and economies of scale
Pretty sure that the US Federal government is the most indebted entity on the planet, and they'd be subject to exactly the same forces that have currently made them upregulate the cost of healthcare.
There is no reason to think they'd use a good bargaining position to bring down costs - the US Federal government is the most cost insensitive entity in history. And a free market is totally capable of finding economies of scale if it is cheaper.