There have been many cases against anonymous comments.
Popular science removed their comments entirely for a good reason, as referenced in a New Yorker article:
“The editors argued that Internet comments, particularly anonymous ones, undermine the integrity of science and lead to a culture of aggression and mockery that hinders substantive discourse.”
Huffington post brought up To Kill a Mockingbird:
“Lee’s basic claim is this: We are capable of doing far worse things to one another when we do not have to own up to the things we do.”
The cases for anonymous comments tend to focus on the lack of effect restricting it will have as people are still willing to say terrible things in public under their own names.