Its more than just zoning breh , problem is at the core of the education system. I think what your saying is if we put the higher class white school districts with the poor black districts thing would change?
It doesn't necessarily have to be higher class whites, it could be blacks as well.
If you factor in the various variables that plague schools such as Household income, race, disability, class size as well as per student expenditure, you will find that household income is the largest factor behind instability issues at schools. Once again i'm too lazy right now to present the evidence take me with a grain i got a headache right now