If we don't invest enough why are per pupil expenditures highest in poor quality urban districts? Perhaps the "investment" isn't being well-spent--which I believe is Philip's real point in the OP.
$10,300. That is what we actually spend per pupil as a nation.
Look here: http://nces.ed.gov/pubs2010/expenditures/tables/table_01.asp
See the large variance in state and local spending? Much of that is inequality.
To address your question: your assertion is factually incorrect. Some cities spend more in inner city schools, and some spend less. The real inequalities lie in rural schools.