That's a hypothesis that I've seen a lot, but it has zero basis in reality. Wealthy countries have fewer births. Countries that offer benefits and incentives to have kids have fewer births. What countries have the most births? Ones where women are treated as cattle.

Now the interesting thing: those countries also have rapidly declining birth rates. Birth rate decline is a global thing that knows no borders. Even in countries where kids are still seen as free labor, almost nobody is having the 12 kids that they used to.