"Kids need to learn I'm not always available"

This one is true, and it's worth separating from the habit it's defending.

Children do need to learn that adults have their own lives, that a parent on a work call can't be interrupted, that a closed door means wait. That's availability, and teaching it is a kindness. A child who learns that "not now, I'm busy" is a real sentence with an end to it learns that people have limits, and that limits aren't rejection.

The glance teaches something else. "Not now, I'm busy" is a clear message with a boundary. The glance is "yes, go on" with a face that says "not really". The child isn't learning that you're unavailable. They're learning that you're available in a way they can't rely on, which is harder to make sense of than a closed door, and which produces the escalation Radesky's observers saw in the restaurants. The child isn't being taught patience. They're being taught to shout.

There's also a loop here that's worth knowing about, because it can feel from the inside like the child is the cause. Brandon McDaniel and Jenny Radesky followed a hundred and eighty-three couples with a young child over six months and measured how often technology interrupted time with the child, how stressed the parents felt, and how the child was behaving. It ran both ways. A child's difficult behaviour predicted more parenting stress, and the stress predicted more turning to the phone during time with the child. And the phone during time with the child predicted more difficult behaviour afterwards. In a separate study of a hundred and seventy families the same authors found that the interruptions were associated with both acting out and withdrawing in the children. They're careful to say the direction isn't settled, and so am I.

But look at the loop from the parent's side. The child is hard, so you retreat into the phone for a moment's relief, so the child gets harder, so you retreat further. Each step is reasonable. The whole thing is a trap with the phone as the door. If the child needs to learn you're not always available, tell them so, in words, with a time. The glance doesn't teach that. It teaches them to try harder, and then to stop trying.