I would argue that a managers time will be filled no matter what she does. So she could prioritise knowing what her peers do, and acquire the basic knowledge to

I would argue that a managers time will be filled no matter what she does. So she could prioritise knowing what her peers do, and acquire the basic knowledge to understand tech maybe? And then fill up the rest of the calendar. So I'm saying it is up to the manager to either suck upwards or support peers.