The community benefit would arise from entertainment value. Flag and announce each battle in progress; let bystanders witness it remotely and provide color commentary. Or, if the game engine allows it, record the battle for later replay and remixing with entertaining captions. (British gaming blog Rock Paper Shotgun contends griefing of others can be funny, so punishment of griefers should be hilarious.)
Of course, the operator must avoid making the griefer hunt look like a community service. That would alienate every self-respecting sociopath.
Many griefers work confidence games, deceptively cultivating a victim's trust, then betraying it. A deception strategy makes development of that trust more difficult by making the griefer distrust the game itself.
After covertly marking the griefer, the game server could send altered, customized data down to his front-end client. What does "customized" mean here? The adjusted representation masks the true power level of other characters, altering their appearance and perhaps even their communications. To the griefer, the server presents weak characters or inexperienced players as intimidating and powerful. Conversely, the server shows him powerful peers disguised as weaklings, likely targets for the griefer's sport. When he attacks, the opponent's true strength becomes unpleasantly clear. The enterprising griefer would need to simultaneously play a second account - a "witness" - to perceive correctly. Over time, due to their ongoing proximity to known griefers, even witnesses could be flagged and deceived. Ideally the griefer soon grows frustrated and leaves the game.
Unfortunately, there is a technical hurdle. For efficiency, MMOGs today push much of the processing load down to the player's client. When the server takes extra time to customize the griefer's data, this may create lag the griefer can identify.
The solution, and the community benefit, lies in incorporating milder deceptions as universal gameplay. Following the example of Alliance and Horde characters in World of Warcraft, who can't talk intelligibly to one another in-game, the "deceiving" MMOG could systematically distort everybody's perception according to his or her avatar's class or alignment. The griefers would be unwilling lab animals, testbeds for new distortions.
Lord of the Flies
As an extension of this idea, MMOG operators could distort the griefer's perceptions more drastically by removing all player avatars from his client. He lives in a world of his own, a pariah. The only other actual players he sees are the ones who have, like him, been marked as griefers. Dangle the possibility he can escape this oubliette and return to the larger community by harassing the other griefers into canceling their accounts.
Does the winner really get to return? What if he becomes a hardened super-griefer, remorseless and superhumanly cunning? Maybe this isn't such a good idea. On the other hand, you could sell the movie rights.