But, if we are serious about the problem, we need to be honest about the large genetic basis of adult intelligence and then figure out how to humanely encourage eugenic reproductive patterns (or at least discourage dysgenic ones) in the poor.
If the problem you are concerned about is "people with a low adult IQ exist" rather than "people are unfairly obstructed by social conditions from realizing their potential", yes, eugenics would seem to be an important part of the solution.
But for many people, the problem is not which people exist, but the degree to which we harm the potential of certain of the people who do exist.
I would bet that we could agree on many social programs to help the poor. Where we probably disagree is on the amount that we think these programs would help fix the long term problem of poverty, and I might be more inclined to look to see if the program has dysgenic effects that would compound that long-term problem.