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.

In our local schools, they don't make *teachers* responsible for enforcing the bans. Students have to keep their phones in a Yondr pouch. If they're caught with their phone it will be confiscated (and require a parent to pick it up), and the administration will give also give additional consequences such as being banned from extracurriculars or school activities like Prom.

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.

If the teachers and schools cannot implement a phone ban because the students won't listen to them, it might be time to reassess what their purpose is.

A lot of schools implement this by having the students put their phones in a locked pouch when they enter the building in the morning. https://www.overyondr.com/phone-locking-pouch

This generally takes it out of the hands of individual classroom teachers.