Kyrne This is better, because it doesn't screw with privacy laws. I have headaches because of GDPR and privacy laws in Europe because of how Byobu is structured. For spam there is fof/ignore-users, which you should have on a forum regardless of whether or not you have this extension.
While people might think that seeing other users' messages is part of the forum moderation, you have to be careful of how you advertise your messaging system. Byobu (or any other system without end-to-end encryption) is not even close to private messaging, and advertising your messaging like that could get you sued (instead you have to say it's direct messaging).
The only reason why you might need the messages themselves is for the police and courts. Private messaging should be the responsibility of those who message.