[thaumasiotes]

> The richer areas have higher scoring schools because wealth correlates with school scores probably due to a combination of natural ability and a more conducive parental and community environment

True enough.

> Richer areas get less state funding than poorer school districts.

Also true.

> These districts have to scramble to just narrow the gap rather than have more funding.

The necessity of narrowing the gap is not at all obvious; as you point out, test scores correlate with local wealth. But test scores also correlate with per-pupil spending -- and that correlation is (1) small; and (2) negative. This is easy to explain with the model "poor students attract spending", but you also need the coda "...and it doesn't accomplish much".

[babesh]

They need enough to pay for teachers, administrators, facilities, and the supplemental education that better off folks love: debate, music, sports, speech therapy, early reading help, etc... That extra money has very high return.