And this isn't a millions-of-years sort of selection, this is the sort that ought to be apparent in a few generations.

How do you know which sort it is?

I don't think that number of children is really a heritable trait - it's a cultural and economic effect,

Heritability depends on the environment. It is quite plausible that it is much more heritable in the modern environment than the pre-modern one.

the economics of having lots of kids are so bad today

I don't want to discuss this, just to suggest that you might be very confused.