Well the most efficiently functioning welfare states are ones that serve small and homogeneous populations. The United States is neither small nor homogeneous (and it is incredibly geographically dispersed for extra kicks).
The largest country in Europe (Germany) has a population that is less than 1/3 the that of the United States, and more homogeneous than every US state (let alone all of them combined) with the possible exception of Vermont.
And I bet even within Europe you would find the best and most efficient healthcare, education and other public services come from the smaller countries. Finland and Norway likely to better than Germany and France.
Given how many of us deal with challenges of "scaling up" tech, processes and organizations as part of our jobs, I'm surprised more people don't really seem to consider the practical limitations of scale for projects of government.
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.
Not sure what you mean by one state being more or less homogeneous than another. The entities who would be receiving healthcare are 100% human, by population, regardless of state.
Are you working from a different definition of homogeneous?
Citation needed.