I'm in a big city and that is certainly not the case. I can submit preferred locations but ultimately there is a very opaque selection process and there is no guarantee made other than a seat somewhere in the system. I know some families who were on a waiting list for years to go to a school in their neighborhood (less than a half mile walking) and were only able to get in this year because of seats opening up due to city exodus.
EDIT - to add, what does this solve in the Cambridge, MA situation where the entire district has removed advanced Algebra?
There are plenty of countries that you get algebra in elementary school. Saying it's only middle school is overly dismisive to the massive amounts of damage to mathematical education in the country this policy is doing.
It can't be doing "massive damage" to mathematical education, because it has simply never been the case that significant numbers of students have ever taken advanced algebra in 8th grade.
EDIT - to add, what does this solve in the Cambridge, MA situation where the entire district has removed advanced Algebra?