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I'd argue you don't need a study, just reasoning. I mean, a study would be good, but we also have brains on our shoulders.

Learning to read or to do mathematics is like anything else, it takes practice. We know, intuitively from our own lives and observes virtually all humans, that humans perform better with less distractions. It would be hard to learn how to play the Tuba with me screaming behind you. It would be hard to learn chess with a movie playing in front of you.

Phones are distractions. Less phones = less distractions = better performance, smarter kids, more likelihood to graduate, higher average income.