banned

I've seen some forums announce forum bans. Basically, when a member gets banned, a thread is made explaining that "so and so" was banned for "such and such." How do you feel about this practice? If you agree with it or do it, why do you do it? Explain why if you don't agree with it!

Scenario: Let's say you have a member who posts a lot, is popular, and gets a lot of engagement on your forum. But they're a bully and they treat a lot of new people like complete and utter crap. You've asked them not to do it and they do it anyways. Would you ban or discipline them in some way...