I tend to think it’s the other way around in most cases. It’s much easier to be prosperous if you have two kids instead of ten. (This was not true when we were all farmers and needed hands to run the place.)
I can see that maybe the very ambitious are working too many hours and either don’t have time or inclination to devote time to families, but I think more often, it’s the number of children that causes bigger bank accounts, and not the bigger bank accounts limiting the children.
When childhood mortality falls due to improved conditions, so does the number of children being born.
I think you’re right.
The two go hand in hand, at least.