My thought as a University student and only a year ago - high school student:
Phones are a really great learning aid. There are also people who prefer to listen and participate more actively in lessons instead of writing down everything written on the whiteboard, with a smartphone they can just take a picture of the whiteboard.
Smartphones are the smallest thesaurus and translator you can get.
Smartphones can graph or take the derivative of any function you want. Wolfram alpha is a wonderful application.
Smartphones can quickly give you the life background of any author. Which helps immensely when analysing literature.
I've never experienced any real problems at school in relation to phones, as the teacher could just tell you to put it away. They have all the power to give you an F if you don't abide.
Admittedly, I've been both at a good highschool and a good University, but banning phones seems like not taking the time to show students how to use those effectively, and at the same time tries to hide the issue of people just not being interested in their lessons. And a lack of phone won't help you grab their interest. They'll switch to talking with each other additionally disturbing those who do want to pay attention.