Is there any evidence to support this link between the invention of the Creche and the fight against those heresies?

Haven't yet watched the 1 hour+ video, but here's a possibility:

The Cathar/Albigensian heresies included antinatalism, and the timing is right. It was Saint Dominic (1170-1221) who actively confronted the Cathars, yet he and Saint Francis of Assisi (1181-1226) did know each other, and this could very well have been something they discussed. It would be fitting that Saint Francis took this on, with his own affinity for the happy critters around the manger welcoming the Holy Infant.

However, the creche initiative probably was less about human antinatalism per se and more about combating the Cathars' Christological heresies that doubted the Incarnation. Remember that in those times, visual instruction (for example, stained glass windows) was still an important means of catechesis. The tradition of the Christmas creche at its start may have had the same intent in teaching common folk about how The Word was made flesh.

Good thing the creche tradition has survived and thrived to this day; it's probably what most strongly has helped to instill this understanding for many small children!

PS - There's another thread today about this same topic. Matthew, does a merge work? Thanks!