Realistically, even car insurance isn't quite "free market". I can't reasonably buy car insurance that covers my car in case of nuclear attack, for instance - that insurance just doesn't exist for most mere mortals (sure, someone with resources can sell a policy at Lloyds, and get it insured - I can't).
Health insurance is even less of a free market. I get what my employer selected. Sure, I could personally buy insurance in addition to that, but realistically, it's not a real option for me or most other people. I'm not going to pay twice for insurance - I don't have the money to do that.
The free market works best when both sides of a transaction need each other equally badly. Those are transactions that don't need regulation. When I sell a car to a private person, they need the car, and I need their money, so it's going to generally be a fair transaction - I hurt myself if I try charging too much. Something like electricity is the exact opposite - my $50/month payment to the electric company isn't enough to change how they set their rates. If they set them too high and lose my business, but get enough other business to make up for the lost (maybe 20 fold!), they would raise the rate. They don't need my payment as much as I need their service. That's why we regulate utilities. Where the needs of the two sides are unbalanced, abuse can easily occur.
Insurance is typically one of those things where people need it far more than the insurance company needs an individual person's business. So they set the terms, not me, and certainly not me and them negotiating it together to find a mutually acceptable deal. I have to take or leave what they offer.
I believe in the free market, but only when it is truly free. Having multiple companies selling a product isn't enough to make it free, however.