I don't see anything wrong with expanding Medicare into a single payer system of universal healthcare. You still have private docs and private hospitals. You just eliminate that 20-30% raked off the top as profit for insurance companies, thus getting more bang for the healthcare buck.
I don't think you have that, and you'd still have the problems, if reduced, of medicare declaring the prices somewhat in isolation of actual costs.
Still plenty of opportunities for fraud, waste, and abuse though.
Personally, If I was a doc I'd be looking at the problems docs over in England are having, not at the rest of Europe. We seem to fall into their models a lot.