All population data for the last century disagrees, and no magic is needed to explain why: the cost of raising children in modern society is so high and the child mortality rate so low that there is strong societal pressure to have less children. Sure, some fringe groups can resist this in the same way that the Amish resist electricity, but this will not be mainstream. Even the Haredim are having less children than they used to:

https://www.ynetnews.com/articles/0,7340,L-5439005,00.html