I think that's the wrong read.
All sorts of animal population follow a sigmoidal growth pattern where there's exponential growth, some degree of overshoot and then a return to a steady level somewhat below that peak.
I think it's more likely, drawing from biology, that we end up at a stable global population level without having to worry about moving backwards along the metrics of education, income or contraceptive access.
Remember it was just a few years ago everyone was absolutely terrified that we would grow to the point where the world simply couldn't hold us all and we'd die off -- and now we're terrified the population will zero out. In reality, neither is very likely. We're probably just going to chill around 8 billion or so until/if we go multi-planetary.