Our insurance companies are for-profit. Wrap your head around that for a moment. There is a labyrinth of regulations surrounding the health insurance industry, but it was one that the insurance companies created through lobbying.
Basically they created a maze between you and the healthcare provider, and both sides need the insurance company to guide you through that maze. The insurance company does it, but they stick their hands in your pocket and the Healthcare provider's pocket as well. To compensate for the theft from the insurance company, the healthcare provider charges unreasonably high prices. For those who have insurance, those unreasonably high prices act as a deterrent for you dropping your ever-inflating insurance coverage. For those who don't have insurance, those high prices are a nightmare of debt and collection calls that often lead to bankruptcy.
Of course the insurance industry is not a free market, both the healthcare industry and the insurance industry are highly regulated. If they weren't, the hospitals would stop and bargain with you as the ambulance were on-route. Nothing would stop them from charging you 500,000 to treat your heart attack, bullet wound or whatever, and you'd be free to choose to pay or die.
A lot of posters like to bring up how much the US government spends on Healthcare, but most of that is subsidizing the profits of the insurance industry, healthcare industry, and big pharma (one of the largest expenditures in our healthcare budget). The US spent about 17.4% of it's GDP on healthcare in 2016 (8.5% on public healthcare spending, and 8.8% on private HC), which is much more than most countries, and even 5% off of 2nd place Switzerland, with 7.9% public spending, and 4.5% private spending).
All that extra spending could be justified if our healthcare outcomes were the best in the world...Sadly:
https://www.internationalinsurance.com/news/ranking-top-eleven-healthcare-systems-country.php
We're number 11. Even in timeliness, which people like to bring up (wait times and all that shtick) we're number 5.