Canada is larger, more geographically dispersed and less homogeneous than the United States, and yet manages to have a functioning single-payer medical system.
Larger by land mass, perhaps, but much smaller by most other measures. And substantially more homogenous (not sure how you're getting a different impression). "Functioning" is maybe a decent description and a pretty low target.
I would not consider 80% white Western European to be as diverse as the US. I don't think the Canadian French thing contributes a whole lot to diversity.
