Economic success is associated with reduced fertility, not greater fertility. (And it's almost certainly causal.) If regions don't have economic miracles, that will mean higher population, not lower.
If you want to have a family four children, I'd think it's pretty universally agreed that it's better if you only have to give birth four times to do it than five, because all four babies survive childhood.
That doesn't negate that there are other factors, especially in countries that already have low birth rates and high childhood survival rates. It was just a factor I hadn't paid much attention to before or heard people mentioning very often.
Hell just high speed rail could encourage populating less desirable areas if a 30 minute trip to the beach was a weekend event.
If you are precarious now, but expect or hope to be better off in future, you will delay having children. If you don't expect better prospects, then children are the best available investment in your future.
If you give people resources conditional on them having children (e.g., free child care), they will of course on the margin have slightly more children. But it's a mistake to interpret this as "financial precarity" causing reduced fertility, because if you give them more unconditional money they have fewer children.
> If they [developing countries] do utilize it [economic opportunity] well, the population is predicted to drop, ...