> I think the costs will go down when the whole nation is the risk pool.

I think this is a justifiably correct presumption if you assume that costs are normally distributed. Are healthcare costs and risks normally distributed?

We had this problem where the cost of financial risk was assumed to be normally distributed and we built a lot of policy on that, including pooling financial entities into bigger and bigger codependent pools, but everyone seemed to have forgotten the known-for-centuries-fact that financial risk has infinite variance. Of course it turned out okay after we bailed out a bunch of rich people.