If the US system was a private sector system it would still be an example of one. Hardly the basis for ignoring private sector health care. The public system is overwhelmed by the performance of the private sector supplying us with goods and services. Except health care and education.  Both healthcare and education in Canada are  expensive.

Compare that with goods and services from the private sector. There is a wide range, at various costs for all goods and services. So the private sector should provide health care and education at reasonable cost. The evidence is overwhelming. 

Evidence against is one. One US system. With a medical system which is the best in the world. All it needs is a tie to people.  A guaranteed Annual Income for the poor would solve that problem. About 85% of Americans have health coverage insurance now. That sounds like the system must be affordable, contrary to media coverage.