First off. Look up the word "eugenics" and understand its meaning.
Second, the issue of buying into "good school zones" would not happen if money was equally distributed among all schools, as it damned well should be. Poor children do not deserve to be damned into an eternal cycle of poverty through enforced ignorance.
Third, what you're describing is a caste system, which I will admit the US is all too close to having. And it is complete, utter bullshit. I need direct you no further than current events to illustrate the problems that forcing a large segment of society into an underclass of ignorance can create.
There will never be complete fairness. But we can do a MUCH better job of equality of opportunity. Just because the outcome won't be perfect does not justify inaction.
1. I know what's eugenics, and I wasn't mean to mention it to reply Dave, I just mentioned it since it was brought up previously. But to certain degree, eugenics can be good. The prevention of inbreed is an example of good use of eugenics. Also, eugenics in a higher level (economy level, for example, taxing additional children) guarantees only people rich enough to provide good education to their kids are allowed multiple kids, this prevents poor people from doing "kids lottery" (having many kids, expect one to be success and change the fate of family) and creating more poorly educated people to drag the society.
2. Giving children of social elites better education excites people to work hard and make privilege to their next generation. After all, all species, from micro organisms to human, are evolved in a way that the sole goal of an individual (in an evolution perspective) is to preserve the particular gene that individual carries.
3. In a caste system, lower level people almost never have a good chance to change their family's fate. What I've mentioned is an Elitism society which a poor smart kid will, in the education system, shine and have a chance to overcome fate, and a rich stupid kid can lose their family fortune. However, to excite people to work hard, there should be a higher chance for rich kids to success while not completely blocking poor kids from changing their fate if they are good enough. For those poor and stupid kids, let them sink to the bottom and just become nobody. Rich, good looking, hard working, smart, sophisticated -- pick at least one. If someone doesn't have any, then what good does him do to the society?