We don’t really have a free market system in this country. The primary determination in how and where you get your health insurance is who you work for. And this is the case because the government intervenes in the market with tax policy and practically forces you to get a provider through your employer.
You don’t actually personally shop for the service, you generally don’t compare competing companies, have a variety of available services, etc.
People often can’t make good decisions on their insurance contracts because they don’t truly understand what they’re paying for the service, nor do they understand what they’re getting from the service until some company decides to dump them when they get cancer because they forgot to dot an I on their application.
Free market incentives do not line up well with the current health care market. You could make a case that in general the nature of medical services do not line up well with free market incentives, but you can’t use the failure of the current system as proof that a free market system has utterly failed. We’d probably be better off with either an actual free market system, or a government run system - this half-ass intervention that only exists because of the status quo and the influence of lobbyists is the worst of both worlds.

