Not only is it a completely conspiratorial claim, the much stronger argument against it is simply looking at a region of the world where elites still heavily advocate family centered norms, i.e East Asia.

In those countries the other social strata don't happily follow suit, young women do something else, they opt out of family formation altogether. If you go to South Korea and ask pretty much any young educated woman why she doesn't want kids or even a relationship, the answer is that she'd risk being trapped in it and disadvantaged at work. The same is true in Iran or Turkey which now have lower birth rates than France.

This stuff has nothing to do with "elite values" or "luxury beliefs", I'd say it barely has a cultural component. As education levels and absolute incomes rise virtually everywhere people change their values.