I support a parent's right to choose for their kids, but this seems very naive, and not far off the "No good will come of you spending all that time on the computer, go outside and play" line my own mother used to spin, and the fears that having computers in the house would warp kids of the 80s.
In reality I had no deficit of outside time, or sports at school, she just took against tech early on. She just got a (dumb) mobile phone about two years ago and rarely uses it.
The real root of the fear here seems to be that your child might have a different upbringing to your own, one you don't understand.
I have no doubt the kids will be fine, if a little peeved at Mom for denying them common forms and channels of social interaction their peers indulge in.
Yes there is a risk of having to have that unpleasant convo with your kids about whats right and wrong and being responsible with your phone..but isn't that what parents are suppose to do? Teach your kids what's right and wrong instead of just denying them of things you don't understand?