By taking just a few moments to refrain from cramming one more thing on your device before a meeting, you could have a much more productive meeting that adds so much more value than the things you would have done on your device.
The goal of team members and colleagues is to add value, skills and expertise. Managers can and should enable and even unleash their people, but they cannot control them. I am not the boss of my team, but I am available for feedback and input.
Human beings aren't designed to do two cognitive tasks at the same time (much less three or four). The research is clear that we're far more efficient when we do activities sequentially, rather than simultaneously.