It seems like there's an easy way around this problem. Praise people who are responsible and financially well-off for having more kids. These traits are correlated with good genes and IQ, so it'll have the same effect.

It seems like we already do this to some extent. I hear others condemning people with who are irresponsible and low-income for having too many children fairly frequently. It's just that we fail to extend this behavior in the other direction, to praising responsible people for having children.

I'm not sure why this is. It could be for one of the reasons listed in the OP. Or it could just be because the tendency to praise and the tendency to condemn are not correlated.