The problem with this is that states are very poor boundaries for almost any economic and demographic indicator: A US state is a mostly arbitrary collection of rural, urban and suburban people, which happened to be put together a few hundred years ago, and which have relatively few economic ties with people from different groups. A big difference among states is just how much of each group we get, plus a small multiplier between big, successful metro areas, and those that are not. How different is it to live in northern Illinois, vs south east Wisconsin? It's still really the Chicago metro area, and the state is mostly irrelevant. The same on both sides of the Kansas City metro.

When you are measuring income inequality within states, all you are seeing is that the largest metro areas are in almost all cases getting richer, while rural areas poorer. It's not a matter of rich states and poor states at all. For almost anything that matters, those state lines are just confounding your statistics.