Poorer places usually have lower costs for things like real estate and child care. Richer places tend to get “cost disease” especially in real estate.

This in turn means that people have to have higher level careers and usually two earners in a home to afford the cost of living.

Overall this all raises GDP but it results in an environment that is hostile to family formation.

It could be a feedback loop too. Fewer kids might coincide with more career oriented lifestyles which drive higher earnings but also bid up real estate and other costs, and so on.

In many parts of the world, it is common for grandparents to take care of the babies and even small kids. In other words, free daycare. Not so common in the US.

As people delay parenting, this option becomes less available. When people routinely had kids in their 20s, starting age of grandparents was about 40-50, when they were still had a lot of energy to help. In a world where people have kids in their 30s, the average grandparent has their first grandchild between 60-70. It means a sizeable fraction of them may be already too frail or even already dead, to contribute significantly in childrearing, needing assistance themselves. That compounds the problem, because then people have to raise small children at the same time their elderly parents start to need more assistance.

I wonder if we define rich/poor by real-estate affordability instead; will this change the stats? Many poor countries have extremely affordable housing even for their poor. Be careful of their homelessness stats, though. Because as a homeless in many of these countries you can go and build your "crib" with stuff you collect around. Many people live in these conditions but it's a legitimate home.