What would you do in that emergency they mentioned?
Gosh. Call the school, maybe? Or one of the hundred other methods via your smartphone (and not).
Why should kids not be able to use them at lunch?
Why should they? Can't kids, who have less self-control than you do—I'm assuming WAYYY more than I should here—have a chance to develop without a smartphone during what's normally a social moment with peer interaction? Are you that bonded socially to your cell?
If you want to control your kid’s phone time, there’s already apps for that.
Yes, there are. Apparently they're not being utilized in a effective manner. Parents won't do anything about it. The school try to educate but incessant attention robbery, be it on an individual level or class-wide, prohibits that. I think the Great State of Indiana has every right in protecting and maintaining a social promise to educate their minor-age children and help them develop in a healthy manner, mentally and physically.
After 18 years old, you can fuck off.