How many parents, who probably paid a lot of money and work two full-time jobs to live in the "good" place so their kids could go to the good school, are going to be OK with this experiment? Do you plan to force them, if there aren't enough volunteers to get statistically significant results?
30 percent of children in San Francisco attend private schools — the highest rate of private-school attendance in California, and the third-highest in the nation
All school is private. Sometimes you pay tuition, which seems better for accountability, and sometimes you pay more for housing. That people send their kids to school is unfortunate. It seems like if you took the daycare out of it, school would not be structured the way that it is at all. It is a source of daycare for children first, and an attempt at productively using that time second.
The thought experiment isn't doing the bussing (effectively impossible as others have noted). The thought experiment is how would you present the resulting data.