All research based on smartphones is based on anecdotal evidence.

It’s even worse if phones are on even without any sort of notification, like vibration.

This is false. There is minimal acceptable evidence that a phone that is online, in a pocket or purse, in a complete silence mode configuration, with no vibration or sound, affects anyone negatively.

I thought you were for banning use during instruction time.

All time spent at any K-12 school institution or local country equivalent; including transition time; is considered instructional time. At least it was by any school principal I've ever spoken to, many of whom were holders of American PhDs in education. Laws in all 50 states reflect this typically.

I think children must be taught how to self-regulate with phones for sure. Much like anything and everything; children must be taught how. I personally never struggled with this because all campuses in my home town would confiscate it at least until End of Day. Sometimes they'd attempt to hold the device longer; but that just resulted in parents going to the police and them being forced to return the item. They'd sometimes hold the item until your parent retrieved it however; and that was allowed as long as they returned it the moment the parent requested it. So you really couldn't rely on parents retrieving it too many times.

I did however get the entire district policy hard limited from "on school grounds" to "In building, from bell to bell" because of the aforementioned involvement of police.

Similarly I will point out we had devices like Game Boys and other portable consoles growing up in the 90s.