pretty much the reverse is true. Families are large in countries that are broke and have weak states (the only ones still growing) because family equals insurance and welfare. This dynamic is also true within rich societies. (marginalized migrants living outside of state support systems have large families, educated affluent citizens fewer)

In countries with extremely supportive states and low inequality like Finland the birth rate is very low still. (1.4). It's simply a matter of choice.

That would usually mean birthrate goes up; fertility tends to decline both with overall prosperity and, at any level of prosperity, strength of social safety nets. Both collapsing would not explain declining fertility.