There are also devices that translate handwriting to digital documents. You have them searchable, editable and safe.
While I agree that you don't need mobile phones in the classroom (you can organize stuff later), they are necessary to organize life. Also schools already use email, share documents and appointments digitally.
That said, I cannot live without my calendars, emails, quick access to important documents and family chat I use daily. I can absolutely live without a pen. The only time I really need it is when my (non-digital) signature is needed.