You don’t really want a true free market. You want a market with full price transparency. You want a market with lots of competition, and where no one in the market can get an unfair advantage over anyone else. And that only happens if it is a well-regulated market, which is a lot like a well-regulated militia.
Usually when people say something regarding the "free market" they aren't calling for abolition of the government in it's entirety unless they explicitly mention such, but loosened legislative measures taken on a specific segment of the existing market.
This system works relatively well and is particularly good in case something goes wrong and you need to spend some substantial time in hospital. And if the worst happens, you get the comfort of knowing that even though your family will lose a part of the income coming from your work, at least they won't end up in huge debts from medical bills.