I had to edit down the original question to ensure that only one question was being asked.  I do believe that the other question of how to fight a war on poverty can reveal some interesting points, so I invite you to resubmit that one.  I tend to think that the desire to end poverty should be in governmental interest.  If one accepts the premise that so many crimes are caused because of a lack of socio- economic opportunity, then ending poverty is something that helps the nation.  Government should see it as an imperative in terms of seeking stop poverty.  A war against poverty could help to make the nation better, and in the process demonstrates how important it is for government to take the lead on this fight:

Critics will say that the United States does not have the money... for decent housing and edu- cation and health care for all, for a Marshall Plan [the United States’ effort to rehabilitate Europe after World War II] for its poor. To them I say we cannot afford not to enact these measures. Moreover, we are spending the money now in other ways. We are spending it on jails and prisons; we are spending it on treating tuberculosis and lead poisoning.

It is in government's interest to ensure that poverty is stopped.  The condition of poverty creates much more painful ways in which government ends up paying the price.  It stands to reason that taking a proactive stance to end poverty could avoid these painful tolls from being paid.

I would also suggest that there is some level of spirituality evident here.  While a secular nation, ours is one where the basic beliefs of religious faith are embodied.  In the allegiance to the flag we salute, there is belief under religion.  In the courthouses where justice is weighed and balanced out, there is a trust in religion.  Even in the money we use for daily life, there is a religious inscription on it.  Hence, it should also be present that these same religious elements, concern for the poor, love of thy neighbor, and the belief that there is something larger than ourselves at play here could help to drive a government effort to end poverty:

We help people, not because they’re Catholic, but we help them because it’s part of our faith. Jesus wasn’t neutral on people. He had a preference for those who were poor, those who were downtrodden, those who were outcast, those who were on the margins. And if I call myself a disciple of Jesus Christ, then I best follow that example.

In this example, one sees a moral or ethical reason for government to lead the way in a war on poverty, something that helps to complement its sociological need.