Precisely. Rational people don't purchase a 400 thousand dollar house in a "good" school district and take lightly to having their kid shipped 30 minutes away to a poorer school district just to achieve some kind of abstract numerical "parity".
You could of course fund schools through sales tax and redistribute funding equally, but then the "rich" districts will just voluntarily fund a supplemental budget to kick the quality of the schools back up to what they were befor. And vote down any further increase in sales tax, of course.
So its quite a connundrum, isnt it? You could , however, issue vouchers or prop. tax rebates, and those "disadvantaged " students who can meet the requirements of a private school could transfer out of their degraded public school, but that will always leave somebody behind anyway, wouldnt it? Not everybody can meet the extra tuition, entrance exam reqts etc, can they? Egalitarianism is such a difficult and elusive goal, but as long as you got your hands on the Public's purse strings, what is there to lose?
The only way it can be achieved is through some redistributive scheme - the wealthier must subsidize the education of the poorer. The problems are just as you outlined. But the alternative is worse.
Education doesn't have to be "equal" across all dividing lines. It just has to be good and getting better, and has to guarantee that those with real talent will advance - just as is the case with sports or beauty.