And if you push this logic to its extreme we would have to take children away from under achieving families to break the reproduction of under achievement cycle. Will probably work but not exactly desirable.
Subsidise embryo selection for IQ for the poor:
Any given couple could potentially have several eggs fertilized in the lab with the dad’s sperm and the mom’s eggs. Then you can test multiple embryos and analyze which one’s going to be the smartest. That kid would belong to that couple as if they had it naturally, but it would be the smartest a couple would be able to produce if they had 100 kids. It’s not genetic engineering or adding new genes, it’s the genes that couples already have.
[Western] Capitalism does this by concentrating wealth with higher "achievers".
If you're wealthy but less fecund you have more wealth to support each child than someone who is either more fecund or less wealthy.