Agree completely about it being invasive to ask. My point is that if my directs trust me with (volunteered) info about their most treasured non-work priorities, then they'll be more likely to trust me when I need them to reprioritize. I think we agree with each other; my point is descriptive rather than prescriptive.

Put another way: If I clearly don't care about their families, then I clearly don't care about their families.