I think sometimes even if teachers can't sort problems out, they can't fix bullying completely.
For example, I was getting picked on by a group of girls whose group I'd left (after one of them sparked a religious debate, which I'd apparently ignited), and they were constantly picking on me, and targeting another one of my friends. I approached the principal, who told the girls off, however shortly after this had happened, they started up again, and it got to the point where my Visual Arts Body of Work was sabotaged (but thankfully salvagable).
Although I do agree that some teachers are lousy and useless when it comes to bullying - sometimes they don't bother sorting anything out ("I'M SOOOOOO BUSY"), and have a 'chat' with the kids. Such as the deputies.