1. once you start kids down the path of mobile devices, it's REALLY hard to slow them down. The sooner you give them a gabb watch, the sooner they'll want a phone. And then you'll have that battle on your hands.
2. Kids' anxiety is in part fueled from the feeling that they are being completely monitored by adults all. the. time. Lots of recent psych research on this. What did you do as a kid? If you were like me, you were wandering over the whole city and didn't come home until dinner time and mom didn't know where you even were. It's not healthy for kids to know that mommy is a phone call away all. the. time. They need to develop the confidence to play unmonitored.
Let kids be kids, and keep them off the devices. The truth is, THEY don't need them. WE want them because WE are anxious. So remind yourself this anxiety is YOUR problem, and you need to resolve it within yourself ... don't project your anxiety onto your kids.