> (1) Supervise the children of working adults, without interfering with their work day.
That is indeed an important objective. I want to underline that it is impossible to achieve it in practice. Each parent has a different life with their own constraint, but each school can only have one time. The complexity of school assignment and start time choice is to find a way to do as well as we can. Unfortunately to the best of my knowledge, there is no perfect solution.
Some school cafeterias even serve breakfast--mostly for kids with subsidized meals, who may not be able to eat regularly otherwise. That is state or federal money available to open earlier. Youth diversion program money can keep a school open later. It is entirely possible for a kid to be at school continuously for 12 hour intervals, every weekday, with no additional burden on the local taxes. Meanwhile, in the suburban schools, the clubs and extracurricular activities are powered by fees paid by the parents directly, and some kids get picked up and dropped off by private cars, as part of their parents' commutes, never even seeing the inside of a school bus.
"Trying 10^120 options..."
We can stop padding our writing to make page length and column inches now. Digital media has a page area that is exactly as large as you need it to be.
If you're a journalist, even in long form stories, your working vocabulary is essentially the 3000 most-used words, and anything outside that should be easily understood from context alone. If you have to follow a word with its definition, you need to write something else. I don't know who edited this, but their iron palm of author-correction should have started the smack after "novem" and finished it before reading to the end of the "illion". A large number doesn't need a large word to describe it.
The essence of the problem is this. Balance the following factors:
(1) Supervise the children of working adults, without interfering with their work day.
(2) Transport those children between their homes and their schools, at minimum cost.
(3) Teach the kids how to be working adults after they graduate. (3a) Prepare a fraction of the kids for further education, to associates or bachelors.
In light of research into school start times as a factor of academic performance, they asked some MIT grad students to improve on goal (3) by giving high-school students later start times, with minimal impact to (2) from the new bus schedules. The algorithm devised to do so failed to sufficiently account for goal (1)--with all of its obfuscated hidden requirements--which made the whole plan fail.
They simply forgot, or never knew, that the primary purpose of public education in the US is to allow both parents to work outside the home, and to subsidize companies that have extended business hours with state-provided supervision for the children of their employees--a benefit usually paid for by the employees themselves via the property taxes on their homes.
The technical solution is easy. The political solution, which includes an admission that this is one of the goals baked into the public schools system, is nigh impossible.