I love that idea, but not sure it's possible to do effectively at WDW, unfortunately. Honestly, it frustrates me, too, because I like to use my phone as little as possible in general, but especially while on vacation. I can't do it on a Disney vacation, however. The app and the weather forecast are too important. It's also my camera.
But there are things you can do - remove whatever apps would be distracting, turn off all notifications, even visual ones (the little red circle on iPhones). Put the phones away when you're in the hotel room. Make an agreement that you won't play around on phones in lines, etc - only use them, not play on them. Maybe leave them behind sometimes when you head to the pool, Disney Springs, a TS dining reservation. I think there are creative ways to limit phone use without having to limit the usefulness of your phone.