I don't disbelieve the cultural influence myself but I'm pretty sure that urbanization matters.

I think the master narrative of human civilization is that almost all of us had ancestors working in subsistence agriculture a few generation ago who have moved or are moving into urban areas. This transition is largely complete in the US and Europe, happened explosively in China post-1980 and is about 2/3 complete there and is less far along in Africa and South America. Birth rates go down in this process.