Any place in the world worth living – except the United States – have universal health care systems.
There are public only ones, like the United Kingdom.
There are private only ones like Switzerland.
There are hybrid public/private ones like France.
All of them share one characteristic: they are not for profit systems.
Until that design point gets brought to the discussion of universal health care in the United States we are kidding ourselves.
The idea that prices will be controlled by competition in a profit driven health insurance system has been pretty well proven to be a fantasy.