I doubt if this could work, I'd reckon policing it would be a nightmare. I agree with hunglee's point that it's draconian and authoritarian.

Nevertheless there seems to be a problem even if that's not the way to resolve it.

It's hard for me to put myself in the shoes of kids today as I'm several generations removed but in hindsight I'm glad that I grew up without a smartphone. It's not the dangers that would have worried me (although I accept they're real), but it's the distraction I'd likely suffer—there's just too many interesting things to read about on the internet. (As a kid I spent a great deal of time playing and exploring outdoors and it seems to me that if I'd owned a phone this time may have been considerably reduced.)

draconian, authoritarian regime