It does, but on a global scale this only works as long as there are enough countries with high birth rates.
And birth rates are going down basically everywhere.
They are higher in less developed countries, but still falling.
Go to https://ourworldindata.org/fertility-rate and select some regions, see for yourself. Africa as a whole has declining fertility rates. Even if you look a high-growth countries such as Niger or Democratic Republic of Congo, the fertility rate has been declining in the last 20-30 years, and you'll be hard-pressed to find a country where it has gone up.