However, these programs all happen within the same school. The trouble in the article is due to a single school with a wide range of options being split into several smaller schools, and the predominantly black school getting worse funding.

Programs such as Honors, AP, electives, etc., are the cheapest way for any student -- regardless of socio-economic background -- to receive high-quality education. Without those programs offered at public schools, I suspect that even more upper-middle class families would transfer to private schools or schools in the suburbs.

Consider sports electives: were they not offered at public schools, the only option would be club programs, often costing thousands per year. At a public school, somewhere around $50 is all that's needed for a year's worth of participation, with coaching that can be comparable to exclusive club teams, and scholarships available for even that amount.

edit: Also, because AP programs are standardized across the country, a student that passes AP Statistics at any school will have the same chance of getting college credit at any school that offers it. This levels the playing field a lot.