Right, but the US - with the exception of the 1% - is not becoming more rich.

I understand the generalization of GDP/capita going up = lower fertility. It does appear to hold true from a global perspective. That's a country level statistic though, which does not reflect income inequality within a country. Assuming that the situation is as simple as that is foolish at best and does not adequately explain collapsing fertility rates in poorer demographics.

The Great Recession contributed to the decline in the early part of this period, but we are unable to identify any other economic, policy, or social factor that has changed since 2007 that is responsible for much of the decline beyond that. Mechanically, the falling birth rate can be attributed to changes in birth patterns across recent cohorts of women moving through childbearing age. We conjecture that the "shifting priorities" of more recent cohorts, reflecting changes in preferences for having children, aspirations for life, and parenting norms, may be responsible.

The Puzzle of Falling US Birth Rates since the Great Recession - American Economic Association https://www.aeaweb.org/articles?id=10.1257%2Fjep.36.1.151