It's possible that the things that would motivate people to have children in poor undeveloped countries are very different from the things that would motivate people to have kids in wealthy developed countries. So OP's take could be right for the US but wrong for Chad.

Of course, it could also be true that a certain level of affluence and freedom for women simply results in a strong downward pressure on birth rates, which is what I think is most likely. (I am not advocating for rolling back women's rights).