I've seen too many people in the workplace wall themselves off, actively resist building any connections, never see advancement or try to grasp any opportunities, and then they leave for whatever reason and not a single person in their orbit gave a fuck that that they ever existed.
You're ignoring power dynamics. It's impossible for a manager and their reports to have real relationships and conversations. Asking them questions they shouldn't answer honestly is just self-serving.
A manager who wants to "care" about their employees as people is just doing a disservice to those employees. They can be understanding, they can provide flexibility for employees to take care of themselves, but they can't and shouldn't try to ask employees about their personal feelings.
I drive in Miami proper and EVERY TIME I'm on the road (especially when heading into/out of Miami), I would encounter at least two cars that drives very dangerously (not just speeding, but like cutting across you--driving in the center lane--very closely from the right lane; not signaling and making a sudden right turn into a street in a crowded street; etc. I had to buy up a front and rear facing dashcams, and I sometimes wish I had a button on my steering wheel that would send the last 10 seconds or so of the dashcam recording to the insurance companies or the traffic police.