https://www.pacificresearch.org/housing-costs-drove-the-majo...
not to mention the perception (if not reality) of an unsafe environment
https://ideas.repec.org/a/ebl/ecbull/eb-25-00236.html
and between leftists dogpiling in big cities where their votes don't count and those cities making it close to impossible to build housing that has to be a factor, together with individualism, anti-natalism, etc.
If it were just a matter of population density, not just metro area population, then low-density high-population metro areas, like those on the west coast, would still have high fertility rates, but they are lower than the high-density high-population metro areas on the east coast.
There seems to be a much stronger correlation to culture or general location than population density.
You might want to google those cities, since every single one that I've checked is a small population city surrounded by rural area.
Your argument about cultural influence might be more persuasive if you compared larger cities.
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.