Why do they opt for such a silly scheme over improving the quality of local schools?
Within a school district, teachers are assigned. They rarely get the school they want. So for any given school, an entire district has the same pool of teachers. And yet some schools are much worse than others.
Additionally, people literally buy houses for the school district - if you start to disrupt that system you'll potentially cause a shift in housing values and then you're up against both the rich and property owners and America can't win that fight with its current political system - money carries too loud of a vote.