I have never understood this argument very well. It's not like there's some sort of centralized bottleneck, schools can scale pretty well.

I would argue (this is completely speculative), however, that cities in the US are (maybe?) denser than those in Finland, and that urban planning has a tendency to lay out infrastructure in terms of area more than in terms of population in itself. Hence big cities having stuffed classes. The same effect can be seen in DMVs or polling centers.