While school lunch is a slightly different situation, I think it still applies that without phones kids will be forced to communicate more directly with each other.
Having lived through the horrors of the pre-smartphone days, I can tell you that this wasn't the case. See, for instance: https://i.pinimg.com/474x/1a/a1/7b/1aa17b28aad6df78a2e1d2016... or https://cdn-images-1.medium.com/max/540/1*U36hBj8i-C7JJJxS4M...
(Edit: I should mention that I'm citing my Dad in my head here, who is an embarrassingly social creature in situations where I would never strike up a conversation. He spent a lot of time travelling around Europe in the 70s staying at youth hostels, e.g. in his university vacations.)
I believe this need is fulfilled by things like Tumblr now, where there are close nit communities centred around specific (often odd) interests and identities, who are vastly geographically spread. The same could be said to an extent for other social networks too, of course, including this website :)
You'd be essentially cut off from your friends back home (apart from maybe a daily email session), so you made new friends wherever you went. You'd go down to the common area of the hostel (or the beach bar near your bungalow in SE Asia), and strike up a conversation with pretty much anybody, since everybody there was traveling as well.
Now I can, sadly, verify that backpackers spend their common-area time on their phones, going about their usual business with their normal "friends". With the only difference being that they're now trying to upload photos that will make those friends jealous enough to leave a like.
I think I liked it better before.
Don't conflate what you would do with the general case - I, for one, -might- venture to a common area but it's extremely unlikely I'd ever consider trying to strike up a conversation.
Worldwide, as observed during 15 years of ~6months/year traveling. Most travelers during that period were, in fact, open to speaking to one another.
And again, in the last 5 years of doing trips on several continents, people you see at "the bar down at the beach" are usually looking at their phone, even when seated at the same table as other travelers.
That never used to happen. And I bet if we crossed paths back then and I asked you where you were from, you would have replied. And we may have even had a conversation.
But isn't this subject to mild confirmation bias? Because you won't have seen the people who aren't in the common room.
Never ever done that and I did travelled alone a bit. I know one person pulling this off, all other people I know would not have done so. Once someone tried to befriend me too much, but I found that uncomfortable (personality mismatch mostly).
For that matter, most people travelled with friends or friends groups and not alone.
It is cool that you was such person, but most people were not.
I'm generally all for the ban, though. I think the bads of the phone outweigh the goods in a school setting.