I like anonymity because it puts a focus on what you say rather than who you are
Also context is important for whatever one says, and a statement hanging on its own is rarely very convincing. It can be a red flag (whistleblowing) and it can be inspiring (famous quotations) but usually an argument is stronger as a result of the context from which it came (a culture, a person's stature, reputation, etc.).
That all said, I think we need to have anonymity, pseudonymity, and also verified identity. If we choose to share across those boundaries (sharing Facebook details with another service, as an example) then we have to deal with and accept the drawbacks. We can't expect to have isolated identities exactly the way we want them given that that kind of system would be a quagmire for developers to build...
Even presuming that counter to actual experience the generic trolls are deterred by a real names policy, there are others who become a much bigger problem when they've got access to real identities. Why do you think doxing is considered such a big thing? SWATing, offline stalking, physical assault, etc. are all risks as soon as a harasser has your info. Even worse when you're talking about something like domestic violence support groups there's a very real danger of the abuser escalating if they discover the victim has been talking to other people. That's 2.1 million people in the US alone who report physical assault by a partner in a single year who could really use access to resources without revealing themselves.