I wonder if there's a hidden confounding selection bias here, i.e. "ability of the school to ban phones". This is probably easier in less chaotic schools where the students listen to the teachers, say.
My student tells me that in practice many students don't keep their phone in the pouch, but they are very careful about how and when they use them. Many teachers have a "don't ask, don't tell" policy - if I don't see you using the phone, and it's not disruptive, then they don't care.
There are schools where the administrators are too busy dealing with violence to have time for much else.
Parent comment described them as "chaotic." I'm not even sure I'd describe them as "schools." But to more clearly answer your question: I think it's fair to question what their actual purpose is (and it doesn't seem to be education), but I don't think it was anyone's explicit intention to make them that way.
This generally takes it out of the hands of individual classroom teachers.