About 'better at hiding them'; maybe so; but that will largely be down to how the rule is enforced. Some schools basically just say "please don't carry your phone. Put it in your locker." In those schools, basically every student has their phone in their pocket. Whereas other schools are more strict about it. The phone can be confiscated on site, and in some cases require the parent to collect it. In those cases, compliance goes way up.

As for 'no phones for teachers and admin'; unfortunately, some of the jobs and responsibilities of teachers are done using a phone. Teachers are required to carry a phone during yard-duty, for emergency purposes. And teachers often use their phone to mark class attendance rolls. ... But its definitely a bad look when a teacher is walking down a school corridor staring at their phone while student phones are banned.

As for the reasons for the ban... well, they are many and varied - including all of the things you mentioned. (liability, mental health vs bullying in particular, and distraction from class activities.)