A bigger issue in my mind is the relatively high cost of classes. In places with low college costs for 2 year colleges, the tuition is potentially payable out of pocket.
It would be possible to design systems where we give more welfare benefits if you attend college. As education goes up, women have fewer kids.
I think encouraging welfare moms to get an education would help deter them from having large families, which is one if the things that compounds their problems and keeps them stuck in poverty.
I originally wanted three kids. I ultimately opted to stop at two. The fact that I am educated is likely a factor in that decision.