One issue I see with that theory is that America has been a bit of a holdout on fertility - I believe it has been fairly high amongst developed nations, though it has been in decline along with nearly every other country. I've read that fertility and religiosity are fairly well correlated, and the US has also historically been a bit of an outlier there, though religion is also in decline. I think that would be squarely in the realm of culture.

I doubt that anyone can really say what the cause is at a societal and ultimately global level; I can only really know my own reasons.