Making high performance teams is part of their job description though, and there is research to indicate that teams with strong social bonds perform better.
Those teams develop strong social bonds precisely because their manager doesn't request (force) them to be 10% more vulnerable. That's a 1-way ticket to a bunch of people not liking you.
You can achieve that vulnerability via being a likable and honest person. I think often us technical-minded people forget that relationships aren't an optimization problem and don't respond like you think they would. Just being decent and trustworthy will take you there, saying things like "you can trust me guys!" often has the opposite effect.
Yeah but you don't form strong social bonds through awkward team exercises. The best team I worked on was super high performing and we did end up sharing personal stuff on our spare time eventually (and some of us are still friends years later). That all happened organically.
What didn't work, however, was the office manager's increasingly awkward attempts to force socialising. When at some point we raised the issue (politely!) that this was often distracting, he became offended and lashed out. We later also found out that he was basically spying on us and reporting back to HQ.
It's one of the reasons why I'm incredibly wary of people who try too hard to be my "buddy" at work, especially if they're not peers.
Related: [Goodhart's Law](https://www.oxfordreference.com/display/10.1093/oi/authority...)