Also, simply moving doubtfully would improve the current generation's poverty level, as they'd still be under-educated to compete with the affluent labor groups

Also, simply moving doubtfully would improve the current generation's poverty level, as they'd still be under-educated to compete with the affluent labor groups and still relegated to the same to same remedial jobs even if the parent(s) are aware moving would potentially increase their child's chances for success, potentially increasing their relative poverty. Also, let us not underestimate the value of support networks from friends and family, living in an area may include aid for child care (grandparents/aunts/uncles/etc) and so forth.