> they did not control for medication or supplements

The only way this would matter would be if phones were banned and then also those other interventions were withheld in order to perfectly counterbalance the expected effect of the phone ban. Do you have some evidence that Iceland suddenly decided to reduce these interventions between 2018 and 2023?

This point isn’t even mentioned in the limitations section of the study, so why are you making it? There are more significant potential limitations to this study that they did describe, including the fact that “we also lacked objective measures of in-school smartphone use and therefore could not determine whether bans reduced actual phone use”. (Though that doesn’t exactly matter either, since if the bans aren’t actually stopping phone use, then they are still ineffective, just in a different way.)

> Alternate interpretation: when it's dark for half the year your mental health isn't dominated by phone access.

This is a nonsensical interpretation that seems to me to betray a lack of understanding of statistics. The planet doesn’t experience any more or less sunlight in the winter between 2016 and 2023, so has no bearing on whether or not there would be a detectable effect from an intervention.

You're inventing a plausible-but-probably-irrelevant cause when a more likely cause is mentioned in the study: students were not using their phones a lot in school before the ban.