Anybody who's an admin, volunteer, janitor, etc should display the tag when it's relevant, but should post without it otherwise. They should be able to participate in threads without drawing attention to their status.
As for regular users and flags, you should really only use flags if it's relevant to the post/discussion by similar reasoning IMO. And you should definitely use a flag if it would help avoid confusion in the discussion. People already adopt shitpost flags in context when making a devil's advocate argument for Porky or whatever.