Healthcare isn't a "free market" because of massive information asymmetry (detailed prices for services, consumer education needed to evaluate information), high barrier to competition, and of course the literal product being your life.
Whereas cars are much closer to a free market. Sure, you might need to drive to work, or you can take a bus or other public transportation, ride a bike, walk, move closer or to another area somewhere this is easier to do, find a job that lets you work from home, etc.
If you choose to buy a car you can gather tons of information, pick a product to fit your specific budget, and end up with something that works everywhere. You can sell the product in the future. Contrast this with healthcare where you can't generally evaluate the information, have minimal to no pricing choices (especially in certain time sensitive situations), etc.
How do they seek out the "best place" if they don't have complete information on what it will cost? It would be like buying cars with no price-tags or MRSPs - yes, there will be good/prestigious dealerships with excellent staff who can tell you the technical details about the car that's right for you, but you won't know how much it will cost you until each component manufacturer sends you their separate itemized bills for months after taking possession of the car, and you can't take the car back (5x tires, 2x wipers, 1x engine, dealership charges, factory charges, line-assembly person 30 minutes @union rates, 1x battery, 348x bolts,1x suspension platform, transmission, etc). That is not a free market.
I am sure I could find a better deal on many medical purchases, but the cost to find them is significant. Purchasing the default/readily-available option is often the best bet because of the hours or days required to find a better solution. Spending a few hours to save $100 or a few days to save $1000 is a clear loss to me.
Cars are another extremely complicated product. Society has self-organized to create reputable sources of information on the quality of different models.
We don't need government restrictions and monopolization of spending to manage the complexity of the economy. Healthcare faces severe problems because of governemnt intervention, not despite of it.
With jobs, people with ample financial reserves can afford to shop around, but people who live paycheck to paycheck can't.
With food, well, it depends on how many different places sell food. Fortunately, there's usually no shortage of shops selling food. The market for expensive food is absolutely free, because I can say no and eat something cheap instead. But the market for cheap food does indeed not behave like a normal free market, as any economist can tell you: when prices for the cheapest foods go up, people will actually buy more, because they won't be able to afford more expensive food. And if one company had a monopoly on all food and set prices for all food high, it would not be a free market anymore, though that's true for any monopoly. Still, if it were a monopoly on something non-essential, people could still say no.
A free market requires competition. When no competition is possible, there's no free market. When there's an army of unemployed people desperately hunting for jobs, companies can afford to be picky and underpay them; there's no meaningful competition to hire those people, who can't afford to say no, because the only alternative for them is to be unemployed. This can lead to a situation where even people with a job have trouble making ends meet.
The food market is obviously not free because you need to eat. The car market is not free because a lot of people need to drive to work. The plumbing market is not free because sanitation is essential.
I won’t comment on the relative effectiveness of free vs centrally planned economies, just pointing out the logical fallacy above.