Just ignoring the flimsy SAT metric, there's something most aren't considering in these sort of data. Cell phones enable and are fairly widely used for all sorts of cheating. Banning them gets rid of that, and so if there was no positive effect from a phone ban you'd actually probably expect a slight decrease on scores because of this effect.
So the fact that basically every school region that bans phones is seeing marginal to moderate gains is just huge. And as others have mentioned, test scores are but one aspect of this. Breaks where kids are playing and interacting more regularly are a million times better than ones where everybody whips out their screen and turns into a zombie.
A "million times better," or 0.9 percentiles better? You have no idea.
Of course I don't want kids to be distracted in school. I just think that if things were as easy as a ban, or some other kind of coercion, education would be easy.
You don't need to quantify things like socialization and real life interaction to know it's vastly better than not, and that's not even touching on the academic side of things where you are seeing clear quantifiable differences. Ultimately, education is easy. A century+ ago this [1] was a college admittance exam, which students were expected to be able to pass, and the overwhelming majority did.
It's not like we're making incremental progress over time. Education has become a dumpster fire, and it's getting worse. The solution is simple - stop changing stuff, and just go back to classical education methods that did work, phenomenally. Tech is clearly having detrimental effects on education, so get rid of it in the classroom. Starting with phones there is a mind bogglingly obvious low bar.
[1] - https://graphics8.nytimes.com/packages/pdf/education/harvard...