I hate to point this out, but...
About 16 percent of Americans are not covered by any health insurance. I don't know how many of those are voluntary.
Add in that about 13 percent of Americans that are covered by Medicare, Medicaid, or some other government insurance.
That leaves about 71 percent covered by either job-based or other private insurance.
So in fact, most Americans, a lot more than a simple majority, ARE covered quite effectively by the free market. And quite effectively for the most part.