"religions which incorporate ideals about large families will tend to spread, but the same can be said about non-religious cultural memes."
The only such meme that ever had success comparable to religion was nationalism, but it self-destructed in the world wars.
Rationally speaking, I think it's well established that having kids is a huge chore. Morning sickness, birth pains, changing diapers, lack of sleep etc. etc. etc. If you had any doubt, the first baby will quickly cure you of it.
The only way for people to put up with all this, and raise large families, is to strongly believe, as you say, that they have an important _duty_ to do so. Giving birth for the benefit of the nation is no longer fashionable, but the various gods' appetite for fresh believers has never diminished.
By contrast, there is absolutely nothing in the world view of the "Sex and the City"-watching woman that will ever lead her to raise five kids.