Human populations (and pretty much all populations of complex life where predation is not a significant cause of death) follow logistic growth trends. Sudden population collapses are not normal in nature.
In the grand scheme of things we don't have a sudden population collapse. Fertility rates are at about 1.7-1.8 in the developed world, and we've got population momentum up till about 9B people. If current fertility rates continue we'll have about a 10% decline every generation once population momentum exhausts itself, which is pretty typical of a bubble that overshot its logistic growth limit and then is returning to equilibrium. (See eg. the stock market over the last week.)
We have some additional complexities in that a lot of those growth limits are because of the interplay between economics and population. There's plenty more room for humans on earth; there's not more room within major metropolises without triggering our "It's too crowded; better not breed" instincts. But economic forces needed to sustain those high populations promote concentration and crowding.