Are you sure? People comparing US healthcare costs to European costs don't realize that these are two very different products. The US population is much more unhealthy, yet it has about the same life expectancy as an average European country. This would suggest that Americans actually have access to significantly more healthcare services than Europeans do.
I think a lot of people assume that some of this stuff is linear when it actually seems to be exponential (or super-exponential) in cost. The median American spends half of their lifetime medical bills in their last year of life. That's a lot of money for not a lot of time. Incidentally, American doctors also tend to spend a lot less in this period, indicating that they have a much more healthy relationship with at least one of health or death.
I haven't been particularly convinced, looking at the healthcare systems across the pond, that they are providing anywhere near the same level of service that you get from the ultra-expensive US healthcare system. They are somewhat more optimized for efficiency and the US healthcare system is much more optimized for outcomes - partly because Americans are so litigious and IMO partly because the patient is the customer. That doesn't lead to low costs.