One version of public school choice would be to allow open enrollment across districts. Money would follow students. Schools that failed to attract enough students would have to be closed up and/or reorganized. Schools that were over-subscribed would have to expand or ration slots.
There are some appealing aspects to this but some problems as well. Schools in the lowest income neighborhoods would have to close in disproportionate numbers, putting a burden on parents located there resulting from getting their children to a more distant school. Bureaucracies don't like to amputate parts of themselves, just as socialist regimes (simplifying somewhat) didn't like to eliminate inefficient enterprises.
There would need to be some mechanism for awarding slots in the more-preferred schools. One expects those in the neighborhood would have first dibs.
The biggest hurdle is nothing less than the U.S. Constitution, which provides for one of the most decentralized public sectors in the world (83,000+ local governments, as Doug mentioned). Local government fragmentation is a natural obstacle to open enrollment across district.
In any case, what we would have here is sorting by another name -- those with the means and/or the initiative would get better schools, those without the worst. If the process of "creative destruction" failed to generate good new schools out of the ashes of bad old ones, we have a formula for deadlock and communal strife: undersupply of preferred schools.
Part of the problem is that some parents in fact have little interest in their childrens' education. A number of my friends are teachers. They are only too happy to meet with parents to discuss the kids, but few show up. Obviously work obligations make this more difficult for some than for others, but the lack of even minimal, widespread participation to me signals a problem. From this standpoint, some parents might not be well motivated to favor the better schools to some extent. (Single data point: at the school in my district, a principal was forced out some years ago by parents who were complaining that the kids were getting too much homework.) Some parents could be sold a bill of goods about the merits of a school. My daughter's in a public school magnet -- French immersion program. But from what we've heard, it is worthwhile even if she never utters a word of French for the rest of her life. She'll get a more rigorous education in the company of better pupils. As I was writing this, my wife returned from a monthly parents meeting for which 9 parents had shown up.
The real public responsibility as I see it is how to raise the bottom, which entails more money but also reorganization. This means working cooperatively with unionized workers, not always easy, and tangling with bureaucracies founded on political patronage. To work, choice requires dynamic institutional change and casualties, in the form of ill-served students and dismissed public employees. The arguments for choice of any type are arguments for sorting and finally a distraction.
mbs