While supporting such actions here seems unwise for many reasons,
Actually, I thought about the desire for revenge.
Adam Smith wrote:
"A person becomes contemptible who tamely sits still, and submits to insults, without attempting either to repel or to revenge them. [...] Even the mob are enraged to see any man submit patiently to affronts and ill usage. They desire to see this insolence resented, and resented by the person who suffers from it. They cry to him with fury, to defend, or to revenge himself. If his indignation rouses at last, they heartily applaud, and sympathize with it. It enlivens their own indignation against his enemy, whom they rejoice to see him attack in his turn, and are as really gratified by his revenge, provided it is not immoderate, as if the injury had been done to themselves."
Now, he did advocate moderation in revenge. ("...provided it is not immoderate...") I think we'd mostly agree killing bullies is immoderate, except in cases like pedophilia, rape or mutilation. But the healing effects of reasonable revenge shouldn't be underestimated. And bullies will think twice in the future
The injured party may be too emotional to be moderate or even effective. This could be a job for great friends