I think it's also worth considering that taxpayer funded US government spending on health care is about the same as in a typical single-payer European country. Then many tax payers still have to pay for private health care on top, to actually get health care for themselves.
Yeah, doctors get paid way more in the US. There's a number of changes beyond the payment method that we'd have to make if we wanted to have costs on par with a typical European country.
