The culprit, however, doesn't seem to be raw intelligence as such, but modern western education, which seems to have a dose dependent sterilizing effect on females. In that light, high IQ isn't fertility-reducing in itself, rather low IQ is protective against modern western education.
Also generally, more clever people focus more on quality rather than quantity, and babies are no exception. Norm are 1-3 kids, not because women are not fertile anymore (unless climacterium is reached), rather time & resources are considered.
Even this is very simplistic & dumbed down view on these matters.
I admire the way you phrased this.
The difference in size between educated and uneducated families might be very large in societies that are in transition on the development scale, but I wonder if the same is true in a society that is stable on that scale. Do uneducated families in the West have more kids than educated families, or do they just have their 2.1 children earlier in life?