The serious free market alternative is to decouple health insurance from employment, create a genuine competitive market in health insurance, and (per Friedrich Hayek, one of the greatest theorists and exponents of the free market) have the government offer everyone with high-deductible plan that exists solely to keep anyone from going bankrupt because they fell ill.
Ideally this should be in the context of a Hayek-style abolition of the welfare state as outlined in Charles Murrays' book In Our Hands: replace all welfare programs with one, a universal basic income (about $1000/month plus a subvention that must be spent on the premium of a health insurance plan -- defaulting to the state provided high-deductible plan if you don't buy something better). Murray ran the numbers and it's cheaper than what we do now, and (the reason Hayek thought the only good poverty mitigation program was a UBI) it distorts the labor market less -- the dynamics of what we do now is to pay people not to work, a UBI pays people whether they work or not, so the loss-of-benefits bar to entry into the labor market is gone. Poor folk will be able to take jobs or gigs in the legitimate economy without an effective confiscatory tax in the form of loss of benefits. We'll also stop subsidizing single parenthood, since the UBI would be paid whether the mother has a husband (or live-in-boyfriend) or not, and the economics of scale will encourage household formation by the poor.
