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?