It seems really, really obvious to me that phones are bad for learning, mental health, social connection, etc. But nobody has been able to prove this in any studies, even in ones outside of the school environment. At some point I think we just have to do school phone bans regardless of the science.
What seems blatantly obvious does not always represent the underlying reality. This can also be taken as a chance to discover better solutions to a given problem than banning phones.