Because banning them works better.
If the school wants to teach responsible use, they can provide school-owned phones for use during coursework.
The problem is that if you have a class of 18 students and all of them are looking at their phones during a lecture or while doing practice problems, it is impossible to police behavior by differentiating who is taking notes and who is texting friends, or who is using a calculator app and who is using Wolfram Alpha. It's much easier to just say "no phones" so the teacher can quickly identify who is taking notes (on paper) or using a calculator (that is a TI 83) versus the students trying to sneakily use their phone under their desk.