[Karkat's honestly been wondering the same thing. Both of his parents are staff members and Nepeta was constantly bullied. If he did anything in retaliation to her bullies and Snow found out he could wind up in detention or otherwise.]

I won't beat around the bush. He has the power to upend teachers from their positions should he deem them unfit to teach. He's here to make sure Hogwarts is running smoothly and if he has to prune a few bushes, then he'll do it to make sure the Ministry is still in power.