What makes health insurance cheaper is not paying for as many expensive operations per capita. While there are a host of factors making US health insurance expensive, the critical factor since 2008 is laws: laws which require that the insurance cover patients who will have very expensive operations, and do so at the same rates as other patients.
The primary advantage of a national health insurance scheme is that it can ration its care for expensive operations, and people won't be able to yell "Greed, greed!" at insurance companies as a scapegoat (ignoring that the profit margins sit at about 4%, which is not exactly the sort of health insurance savings that would fix anything).
There is little evidence to support the "US consumes too much healthcare" narrative and some good evidence that our total healthcare spending is inline with our level of wealth [0]. There is quite a bit of evidence to support the "Prices for equivalent healthcare are significantly higher in the US".
The primary advantage of a national health insurance scheme is that it can ration its care for expensive operations, and people won't be able to yell "Greed, greed!" at insurance companies as a scapegoat (ignoring that the profit margins sit at about 4%, which is not exactly the sort of health insurance savings that would fix anything).