Cell Phones are a real danger to education. People (kids in this case) are learning by searching online, rather than tutoring. Setting aside the preferred method that includes actual human interaction, concentration, and real dialog, the other issue of one of fairness, accuracy, and context.
I do worry about things when I hear someone say, "do your own research". This usually means "look it up on the internet", as though the net is a benigm encyclopedia of truth. It simply is not. The vast majority of the internet is driven by commerce, be it selling product or money through clicks. Google results can be manipulated if you give them money - and this is true of ALL the search engines. Layered on top of that are algorithms that control result sets. Meaning, when you search Google, you're getting back the results they want you to get, or rather, minus the stuff they don't want you to get.
This doesn't materialize as you'd expect, because they need you to engage, so the content is "personalized". This ensures you get results from sources you like (either intentional, or not), people you like, shows you like, and web sites you frequent. This in turn creates echo chambers, where we find affirmation (affirmation makes us feel good, and therefore more likely to stay longer) for whatever crack pot theory we've got.
Now, in a wider societal context, this one thing (dangerous, but off-topic here), but in an educational situation it's dangerous. When you consider young minds are impressionable, it's a real worry. So I applaud this idea of "banning" them in schools.
Still, the only way to truly make it work is to kill the signal. Have signal blockers that stop them working in each classroom. It would be trivial to do, and you could exclude certain numbers (say the tutors) from being blocked. However, paranoia is high these days, and besides, it is illegal in the UK to block cell phone signals, so it would need a lot of work to get pushed through.
That said, they could build classrooms that blocked signals without breaking the law (though no doubt it would be challenged if they did). Think of the concept of a Faraday Cage.
There are far too many entitled individuals today to ever get this done. I laugh when people say things like, "but I need to be able to contact my child!!" Why do they never ask themselves, "well how did they do that before the cell phone?"