...most users here like to remain anonymous and private on certain matters and this wouldn’t encourage that very much.
I don't understand how shoutbox would breach the privacy!? Users here comment/pm, the same way they would be chatting? Plus, fwiw, there was this feature on forum I was on years ago where if you would chat by having, "/private" as prefix and that chat would remain private between the two users chatting.
I also do not see how chatting on the chat box will breach someone's privacy. This will only happen when an individual reveal their identity or leak their data themselves.
The major disadvantage I see with the shoutbox is that a few people will hijack it either for fun or any other thing. And after the first few months, people will no longer find it useful.
The forum is just fine as it is, there's no need adding many more things.