I have heard the argument that as Africa continues to develop, birth rates will fall in Africa the same way that they fell in east Asia - leaving no large regio

I have heard the argument that as Africa continues to develop, birth rates will fall in Africa the same way that they fell in east Asia - leaving no large regions in the world with growing populations, and thus no pool of immigrants that highly industrialised countries can pull from - leading to highly industrialised countries collapsing and whatever existential risk comes from that. I personally don't buy it, as trends don't continue forever. Birth rates will never fall to zero, and we'd likely come up with a solution to the dependency ratio problem before the least-developed country in the world industrialises