While I agree with you on the scientific front, I agree with the author on the risk/action cost front. There's not much cost to preventing the use of phones during school hours, it seems to be a net benefit to education and teacher/student relations even if the hypothesis is wrong.
Banning platforms from allowing under 16s to have accounts is harder because kids will work around it very easily, but I would be happy to see it happen anyway, and made Facebook's problem to deal with.
I'm 100% in favor in banning smartphone during school hours.
The big danger is to spread the incorrect conclusion "it's smartphone's fault". For example, if it is social media, then, we need to change social media, not just ban smartphones, because it will not stop social media to do even more victims, and the number of victims will be bigger if people were convinced by the incorrect conclusion.