Collapse, or just local transition to a different model of social/spatial organisation rather than desolation through ecological or man-made catastrophe? It's interesting that Asian complexes like Angkor or Polonnaruwa were experiencing growth and eclipse around the same period - not that there has to be any association beyond a roughly contemporaneous cycle of increased and then lessened population concentration.

But there may be more to the story than that, a recent paper (abstract here) suggesting that numbers recovered in the 15th-17th centuries before declining again, by which time diseases associated with the Columbian exchange may be the culprit:

The indigenous repopulation of the area coincides with environmental changes conducive to maize-based agriculture and bison-hunting subsistence practices of the Illinois Confederation. The subsequent regional depopulation corresponds to a complicated period of warfare, epidemic disease, Christianization, population movement, and environmental change in the eighteenth century.

The old "savage natives" trope of course represented a convenient figleaf for conquest, whether the newcomers sought to "civilise" them or slaughter them. Even confronted with the achievements of pre-colonial cultures, newcomers sought alternative explanations, Great Zimbabwe's most notorious early excavator throwing away centuries of priceless deposits to "remove the filth and decadence of Kaffir occupation" in his search for an ancient Phoenician settlement in southeastern Africa. There's an echo of the attitude in modern-day notions that "xxxx can't possibly have invented agriculture/pyramids".