You misunderstand me completely.
First, the idea that the rich become wealthy at the expense of the poor would only be true in a zero-sum economy. We do not have that.
Second, I wish nobody were poor. To that end, I do what I can to contribute to and support charitable endeavors. I believe that private charity is better at delivering social needs than the government. Compelling me to pay for other peoples needs isn't charitable, it's theft. It's also, when the government is involved, massively inefficient. That's part of the argument for limited powers.
Third, I agree. Military spending is wasteful and inefficient. We should be more frugal with my, and your, money. However, we all know that last thing government is is frugal.
Fourth, anyone who has witnessed America's educational decline and still believes the government can do a better job of education than the private sector is either grossly ignorant of the depths to which we have sunk, or is whistling past the graveyard.
I am in general agreement with your sentiments. I wish well for all men, and I wish to see none fail. But limited government and private relief is a much better approach to solving the problems.

And who decides what is the business of government? You, me, who?

We can all point to the Constitution, maybe the Federalist Papers or even the personal correspondence of the Founders to make points. The fact is that most of us can find clauses in the Constitution that to us seem simply ignored today or perhaps distorted by Supreme Court decisions beyond all recognition. These arguments seem to lead nowhere.

Perhaps we should be looking at conditions and trends in the country and be paying more attention to what kind of country we want to live in. To me, that seems a better guide for what government and people should be doing than to endlessly debate what is the "right" thing to do based on our own sense of right or wrong (never someone else's) or on what the founders thought.

There was a speech on the Senate floor recently that seems to take this approach and that somehow seems related to the discussion here. You might want to take a few minutes to watch and consider it.

//www.youtube.com/watch?v=fQOCfweYLrE&feature=player_embedded