Just thinking aloud.
Could it be that the "stories" we consume (books, movies, TV, games) fill our heads (as in, focus our attention) with ideas that don't overlap much with family life? It's all about single people doing cool or fun stuff, with the occasional tired parents.
I wonder how hard it would be to give credibility to the hypothesis (yeah, "verifying" it would be much harder). What's the correlation between "percentage of time spent on non family focused stories" and "children per woman born in the following 5 years"? Sounds like a super noisy signal. Maybe averaging by country or even city could strengthen the data.
That seems like unnecessary complexity (and also doesn't match my own observations). You're replying here to a theory that it seems to me is sufficient on its own to explain the phenomenon, unless you see some issue with it? I'm not certain the theory is correct but I think it's entirely plausible and more importantly I've yet to encounter a better one.