I disagree; government regulatory practice is mainly taking some of the worse edges off the inherently broken model of "healthcare as insurance". I'm thinking particularly of major conditions. I think regular office visits could probably be paid for out of pocket, but the real money is going towards hospitals, and that's also where free-market solutions don't work at all.
In particular, I don't see how an unregulated system would solve the correlation-across-lifetime problems. A friend of mine was born with a congenital heart defect, a "preexisting condition" since birth. In a free market, it actuarially makes little sense to sell him insurance at any kind of affordable rate, because the uncertain event already happened (he lost a particular lottery at birth). And in a really free market, that would apply to many more people, because rational insurance companies would require genetic screening before allowing coverage (which they currently can't), allowing them to uncover all sorts of less obvious genetic lottery losers. Put differently, the random risk being insured is, in large part, entire lifetimes, which the insurance market cannot handle, particularly if you think individuals should have some kind of choice (vs. some kind of setup where parents have to buy their offspring's lifetime health insurance pre-conception).
Risk pooling across a large corporation's employees is sort of a hack to approximate the needed across-population risk pooling, in the absence of a true socialized risk pool. That hack has let he U.S. hobble through much of the post-WW2 era, since a large percentage of Americans had employment-for-life at large companies, but it's poorly suited to a world of freelancers and job-hopping.