You are underestimating the extent that geographic diversity materially impacts the design of government policy around social services, irrespective of population scale. Social policy is based on a set of assumptions about local needs and local conditions. The larger the geographic area, the less valid any particular set of assumptions are going to be. Two geographically rural regions in the US can have very different medical care requirements. It isn't the "rural" that makes them different but "geographically distant", the latter being correlated with widely varying ethnicities, cultures, environment, and demographics.

Almost any uniform Federal policy would be completely broken for some part of the US due to its geographic extent and diversity. This is a recurring issue for policy that has nothing to do with social services. For example, the fundamental legal axioms around water management are different between the eastern and western US because it would be a policy disaster for that to be uniform. See also the disaster of trying to apply uniform highway policy in the US, which have since partly devolved back to local control.

Social services are similar, including the implementation of medical care and schools. We already have cost problems in some regions of the US where required medical facilities are virtually never used because incidence varies widely across widely separated parts the US, it doesn't average together, a large part of which is explained by genetics, culture, and environment. Every aspect of schools vary wildly from region to region, virtually nothing about it is uniform, because States recognize that maximizing school participation -- a social good -- requires respecting local conditions, culture, and constraints. I grew up across several geographically diverse parts of the US and experienced the extreme range of local adaptation first hand. There were some questionable local policies here and there, but in the vast majority of cases those diverse social service policies were trying to optimize local outcomes.

If there was a uniform and in-depth Federal policy for all of these things, the amount of flexibility and leeway required to not produce objectively worse local outcomes for many people would asymptotically approximate having no uniform Federal policy at all.

All of the European countries you list have a geographic extent that fits within a single policy jurisdiction for both healthcare and education in the US. In the larger US jursidictions, they devolve considerable control of these to more local authorities, recognizing the limitations of uniform policies in large geographic jursidictions.