Turning the question around, I've read and ignored occasional private messages on social media. Often the questioner is asking for a free service, counting on sympathy for what amounts to emotional blackmail. I never respond to those.
In your example of a person in a power position, I can relate as an admin in several social media groups where I have had to ban members for various infractions of group rules. Whether I'd respond to a subsequent private message or not really depended on the tone of the message and frankly with my level of annoyance with the reason they were banned, and whether we had had a previously good online relationship. Belligerent, demanding, insulting, bullying, trolling, entitled attitudes don't get a response from me as those are not behaviors I want to reward. Respectful, sincere, tactful messages always get a response.