A statistical model was used to examine these relationships simultaneously by predicting the likelihood that a girl reports being very happy.

The model includes socioeconomic status, parent–child communication, screen-time limits, and an interaction between limits and communication.

The results reinforce the patterns in the figures. Parent–child communication dominates the model. Girls who report strong communication are about three to four times more likely to report being very happy than those who report none. Socioeconomic status shows a smaller independent association. Screen-time limits contribute little on their own and matter modestly only when strong communication is already present.

If phones were the central problem, limits would emerge as a robust solution across contexts. They do not…

What the compensatory-use model rejects is a stronger claim. It rejects the idea that smartphone exposure itself is the primary driver of youth distress and that prohibition is therefore the central remedy. If that causal story were correct, limits would show large and consistent benefits across households, including among those with the weakest communication and highest distress. They do not.

And to close:

The most reliable way to improve youth well-being is to meet individual needs through connection instead of control.

That work depends on cooperation, not compliance.

Here is the full essay by Owen Kellogg, of course this is only a single study.