I've thought a fair bit about this now and finally understand what point I was trying to make. Educating the poor is not enough because the rich are an integral part of the problem. Just as the poor are so because they lack education, so the rich hold deep prejudices against the poor because of their lack of education. It's just like psychotherapy on an individual scale - the problem is never limited to just the person in question. The problem is the whole family, the whole society, not just one aspect of it.

In other words, our entire society needs to be re-educated in order to solve this problem, not just the poor.

>we would probably start to see the poor creating their own solutions, and further changing our societal structure.

Indeed we would, but we would also see a great deal of resistance to it from the powers that be. This needs to be addressed with equal importance. What's the point of bringing people up when others will just try to push them down more? We need to bring them up and make space to accommodate them.