I'm not convinced that the way insurance works in the US explains rising costs here, because costs in most of the rest of the first world such as the EU and Japan have been rising about as fast as costs in the US for at least at least the last 50ish years.

We pay a lot more per capita than any of those other places, but the ratio of what we pay per capita to what a given other first world country pays per capita has been pretty steady long term.