Schools nowadays deal with a lot of cyber bullying and the like. These students/teachers know who the poster is and who the intended target is in most cases. So there is no anonymity there and people still act like jerks.
I think in reality it is not being anonymous that leads people to be jerks, it is the knowledge that they have no consequences for their actions. The internet seems to be a fine line between no consequences for being a jerk and massive overkill if you piss off someone with the appropriate technical skills (or a stalker I suppose).
Just because anonymous people are jerks does not mean that being a jerk is caused by being anonymous. So really all you are going to do is make it easier to harass people on the internet without really weeding out the people being jerks. So not only is this solution infringing on a lot of rights, real and perceived, it wouldn't even accomplish anything.