Essentially, statistics will tell you how to gradually improve a system that you already have (conventional class-based school education), but won't tell you about the value of an entirely new system. It's a sort of 'local minima' problem like that.
The article admits as much, but fails to acknowledge the other solution to this conflict: instead of a 'phone-free school', why not change the school to support an electronic educational paradigm? Just as the Montessori method or the culture-rich concept of Kindergarten education are usually very valuable to those children who are lucky enough to experience them, there is already a wealth of evidence for interactive and electronic learning methods - not just a 'potential' as the article claims. The key difference between learning paradigms such as Montessori and Kindergarten and electronic education is that the former requires expensive (and safe) access to materials, and the latter is now almost free! The article claims: "However, if there are two or more options for engaging with learning material, then it is best to select the tool that will yield the best results." I ask, what justification is there to not select a tool that isn't perhaps the best, but it the best that society can afford? One-on-one tutoring with experts and fully-equiped laboratories would be wonderful, even better than electronic education, but that was never the offer. Historically progressive educational authorities are literally rejecting an educational opportunity that requires nothing except open minds.
P.S. An irrelevant but interesting nit-pick: the article mentions that you have to hold each word in memory as you read a sentence of English text, but this is untrue. Readers create a mental, semantic and emotional image while they read; dyslexic readers might struggle with the concept of a 'word' itself yet are still able to understand the meaning of a sentence.