I don't think this would help for two reasons. First, so many people have Apple watches these days and don't have any problems having them glowing bright throughout the show.
Second, from my experience, most people who use their phones during shows just have their phone out for a few seconds. Yes, enough to disrupt the audience, the performers, and generally everyone around them. But the point is that these kind of people would say that they are just checking messages because they have a sick child, important work email, are a doctor, need to check the score of the ballgame, etc. So they don't feel that they are part of the problem. Sending a quick text message, checking your social media feed for 30 seconds.....these are getting more and more common as opposed to people sitting on their phone playing games or taking phone calls.
So when people see this announcement about the pouch, many will see oh yeah that doesn't apply to me because I don't use my phone, I just might take it out for a quick second to check if anyone liked my post or if my sick child needs me. And that will completely defeat the purpose of the pouch in the first place.
As for me, after dealing with these tech interruptions so frequently and at every single show, I have officially given up and when I the phones (which are never out for more than a minute at most) I force myself to ignore and concentrate on the stage, as hard as that is.