Yes, in classrooms. This is the first I've ever heard of assigned seating during lunch.
If they're doing it at lunch it's obviously because they've had problems in the past.
The rule is idiotic. And I'm not going to buy the notion that, well, they must have had their reasons for it. Tough cases make bad law -- or, in this case, bad school policy.
I am mystified by those who seem willing to defend any rule whatsoever, simply because "its the rule".
If you don't like it homeschool your kid.
Mine go to a private school. Oh, and they can sit where they want during lunch.
Discipline is not something that should be getting taken out of schools.
There is a world of difference between maintaining decorum, and over-regimentation of this sort. The staff could simply discipline the kids who misbehave, and not punish the rest by not allowing them to sit by their friends. Of course, that would require judgment and common sense.
Good your kids go to a private school and they can sit where they want.
Since your kids aren't going to a public school mind your own business with respect to how they're run and stick to telling the private school how they should do things.
If they aren't good enough for your kids then they obviously aren't worth your busybody time.
You have as much credibility as someone who homeschools does with respect to telling them how they should run their school. In other words, none.