It’s a common justification given, but it’s not true. The same happened in almost every advanced european society in the 80s, when things weren’t unaffordable. Urbanization is probably the largest contributor to this, because children are absolutely optional in city dwellers.
We should stop pretending we can reverse this trend, and the whole doom-saying around it. Instead southern europe needs to plan for the medium-term future, which necessarily include the transformation/abolition of the unsustainable welfare state paradigm built in the 80s.