If they get this power, why do we need the global ban, then?

Because it’s an exhausting waste of my time to police cell phones on an individual basis. Of course, a lot of the teachers in my building require students to put their phones in a basket or in a numbered slot when they come into the room so they don’t even have to deal with it. If you have it with you in the room rather than depositing it like you should the teacher will take it and log it into the office, which means mommy or daddy has to come get little Johnny’s phone on Tuesday or Thursday between 7 and 8 am.