I think this argument would make more sense if it were external constraints that were driving a declining population. But the population is only decreasing because the majority group of people stopped having children. So they will remove themselves from the gene pool, the minority will become the majority, and away we'll go again.

As an interesting factoid the Roman Empire, which for many people of the time would have had some analogs to 'the world', also had a fertility collapse prior to its end, that they tried to combat with quite strict laws, but ones which were ultimately ineffectual. Of course that was hardly the end of the story!