The people who benefit are not the wealthy, who can afford to simply buy a house in the school district of their desire, but simply middle class parents who care about their kids.
Poor people care about their kids, too. They're just struggling to keep a roof over their heads and food on their plates instead of worrying about what college their kids are going to get into.
Assuming we're talking about the US, this is just not true. If you are actually poor, then the government has incredibly generous programs to put food and shelter over your head. Where I live, the city government will literally paid for your daycare and you can enroll in lotteries to buy homes at 1/10th the regular price.
Middle class parents are wealthy compared to the average student of a "sucky" school. These schools are typically the in the poorest areas in the state/county.