Part of your job is to keep kids on a schedule. Shit gets messed up and learning is disrupted for
many students if you don't. It's also your ass on the line if you don't know where kids are, within reason, all day long.
Devices that don't necessarily, but do tend, to make keeping the schedule harder, exist and aren't needed for education.
("What does a CD player at lunch have to do with that?" if enough kids start listening to music at lunch I 100% guarantee you issues getting them to the next class on time increase in frequency a ton, and that's before you consider that every thing you add like that to a school environment increases the rate and severity of, ah, physical disputes)
So yeah, of course you ban their use.
"You could just only ban them for students for whom they're a problem."
Yeah, you could, but now you're dealing with even more angry parents up your ass because "you're not being fair, and you're singling out my kid". And you're burning more time you don't have dealing with these issues ad-hoc. No, it has to be a blanket ban.
Schools could be a lot less authoritarian if they didn't have to serve kids (or parents...) who can't handle a looser approach, and if they could simply kick out very disruptive kids, et c. But they can't, so they're a lot worse, in a lot of ways, than they hypothetically could be.