This does not mean that you do not care about other people, especially those who need extra help. Correction means becoming altruistic instead of egoistic. Therefore, caring for others is "built-in" in the prayer. If you are not praying to become altruistic then you are not praying for correction anyway.
Being poor means being deficient, not having something. But why pray for something instead of working to get it? Because there is one thing that, no matter how hard we work for it, we will never get by ourselves: the Creator's quality of bestowal. So praying for the poor is wanting everyone to have the quality of bestowal because that the only thing they can't find on their one. Those who pray for the poor, for others, are rewarded first.
"Only a life lived for others is worth living" ~ Einstein