Not necessarily busy work, it's just flexible when it needs to get done. I did read your post twice, and it is kinda normalizing godawful management practices.
I don't need to be fully engaged every moment I'm at work. I need to be paid for the time I'm asked to reserve for it.
I think this is fair. It's reasonable to require a stowed phone, and we don't have a reasonable expectation of privacy while driving our cars. No essential liberty is being violated.