“I don’t know of one case where social pressure caused a husband to give a Get. The only thing that is accomplished is that the husband has been embarrassed. It should be noted that the second Bais HaMekdash was destroyed because Bar Kamtza was embarrassed even though he was an evil man. It should also be noted that one who embarrasses his fellow Jew loses his portion in the next world.”
That would only apply if he embarrasses someone when he is not allowed to (which is most of the time). If it’s a situation in which he is halachically required to, it would not apply. I believe there are situations in which a Beis Din may be required to embarrass someone publicly.It’s not a topic I’m so up on, but I think that I have heard stories from the past.
If someone is chayiv misa, they are obviously being embarrassed publicly, so clearly there are cases in which Beis Din can publicly embarrass someone. Nowadays, it’s probably much more complicated, but it’s possible that there are situations today where they are allowed to.