1) They don't show median household income because that would discriminate against the poor, or some line of thought like that. 2) The reason that standardized test scores are shown isn't because people are really interested in the tests, but rather that they act as a proxy for the quality of the area; you don't get much in the way of gang violence in areas where kids do well on tests, generally.

There really should be a better way of measuring the quality of an area, but I can't say I see an obvious one.