There’s several factors I can see involved.
The US healthcare system is the product of government intervention and not (as many on the left and right like to claim) free markets.
Historically there were many mutual organisations which provided healthcare (and other services) to their members. These were grassroots organisations, but under pressure from the AMA (and undoubtedly big insurance and pharma) they were largely driven out of existence to protect the income of Doctors.
Then, during WWII there were wage caps, so employers started offering health insurance in lieu of pay. The government encouraged this, it creates a more servile workforce - you don’t dare make a fuss because you’d lose that important health insurance.
High prices are due toat least two factors - patents which massively inflate costs and encourages expensive research into areas of high profit and the lack of a monopsony, which in countries which have a single health service provider drives down costs in many drugs. That means the US consumer pays more to maintain pharmaceutical profit.
What the natural price of health care might be is unclear - the market is so severely distorted on a global scale we have no way to find out.
Quite frankly, whilst I think the NHS sucks in many cases (getting good treatment is a lottery, many hospitals are sub standard, there’s a surpless of managers etc), I wouldn’t want the US system either, because that is a massive basket case as well…
Surely there must be a better way than both of these?