My schools (all of them) had open seating and free-for-alls in their open areas; at my high school, they didn’t even bother trying to keep us inside the grounds

My schools (all of them) had open seating and free-for-alls in their open areas; at my high school, they didn’t even bother trying to keep us inside the grounds (which meant that we could, and did, go socialize with the neighborhood.) This is in a school system that contains roughly a million students, and (AFAIK) didn’t impose significant differences between individual schools. I can’t imagine assigned seating working very well, except for at a very small school in a small district. Yours might not be a representative case.