Yes, the fact that literally all health care goes through insurance is a big part of the problem. As my dad says, if you had to get all car maintenance done through your car insurance, changing your oil would cost $5,000.
This has been well understood in policy circles. The problem is that the employer insurance payment is tax deductible. This subsidy, along with scale, locks people into employer-based care through insurance. The Obama administration attempted to reform this by reducing the deduction on "Cadillac" health care plans but even that modest reform has since been scraped. (Insurance companies framed it as a "tax increase" when really it was closing a loophole.)
It is not like that at all in countries like Germany and France, where really literally all health care (for a lot of people) is covered (mostly) by general medical insurance. The pricing explosion is exclusively an US problem.
(Germany has private insurance and France as well in parallel, but the main system is "sozialised")
The healthcare systems in Canada, the UK, France, Germany and Switzerland are all distinctive (they’re main commonality I suppose is that they somehow deliver quality healthcare at a fraction of the US cost.). But to hear Americans say we should “do it the way it’s done in Europe” is to understand that the person likely don’t know how the healthcare systems operate in different countries.
The other frustration in talking about this is the tendency to “It’s just” the problems. If this were a simple problem with an obvious solution it likely would have been solved. We are where we are because of a century of organic, and often idiosyncratic, growth. Well intentioned policies of decades ago have come back to bite us with unintended consequences as likely are our best ideas today.
I don’t say we should throw up our hands and give up, but when anyone says there is an easy solution - we just need the political will to let them do what they want - I do see snake oil.