this whole argument depends on the supposition that if brith rates ever drops below replacement rates, then that inexorably implies the extinction of the species. whether or not now is a good time, at some point growth has to stop. and there are plenty of conceivable social arrangement that are perfectly workable with a constant population size.

the only real argument for continued growth in to preserve the current structure of investment. that's your great filter, and it will result in economic collapse which isn't the same as extinction.