If you view the societal/political cohesion/consensus as a process of behavioral survival of the fittest (eg. requiring a certain flexibility to adapt) then taking away the flexibility that anonymous online communication affords your citizens might not be so good when/if it becomes time for the system to adapt. There will be less space to communicate and plan gradual change, skipping that possibility and going straight for more bloody forms of change. Say like the way we did things 200 years ago.
Personally and subjectively, I think this is a dumb and evil thing to do. But not unexpected.