Without government interference the free market would continue to deliver a healthcare system thats overpriced and delivers poor outcomes with millions of uninsured. The free market has failed on healthcare for 30+ years.
If we had a free market in health care, what would happen is rival pharmaceutical companies would make drugs that do the same for cheaper causing a price war. Rival medical equipment manufacturers would flood the market with cheaper equipment causing a price war. More medical schools would open up to pump out doctors, nurses, and other medical practitioners to compete for the insane dollars on the market causing a price war.
The hallmark of a free market is price wars driving costs down. We don't see price wars because health care is a HIGHLY regulated market that is VERY far from being free.
Currently there exists an upper limit on the cost of health care. That is the point where its cheaper to buy a round trip ticket and fly overseas to get the same quality of medical care somewhere else, followed by the slow realization among the American people that going overseas is the best option. There should be a time delay in this process, where medical tourism becomes significantly cheaper and nothing happens for several years, and then the flood gates open and everyone suddenly starts flying overseas all at once as people get informed and get over their fears. THEN we might see radical change to the health care system in the US as they suddenly face bankruptcy with hospitals emptying out.