The per-capita healthcare spending of Europe, public and private, is about half what ours is with similar health outcomes. We are an extreme outlier.

https://data.oecd.org/healthres/health-spending.htm

The remainder of the premium stops going into the pockets of insurance middlemen.

This just replaces one middleman (insurance co) for another (government).

I can tell by the downvotes that my point whooshed over everyone's head -- my point was essentially yours. Changing who pays isn't going to change anything. We have to change what gets charged.

This is substantially easier to do in a single-payer style system.