>I usually assume that this USA-specific "missing middle" of dense housing is a result of car culture and the suburban nightmare we've created across the country

I suspect the layout of European farming communities is a holdover from feudalism, when serfs worked the land on behalf of the lord of the manor, who owned all the land.

They probably found conditions in the New World much more desirable, where they could own their own farm. And when they owned their own farm, they probably found it much more convenient to live close to the fields and barns and livestock that they also owned.