User blog comment:Rappy 4187/Technical Update: April 19, 2017/@comment-30109486-20170420124425/@comment-28391659-20170422031414

Personally, I would not remove WikiActivity from the header for anonymous user because removing it would hindering new editor to come in. The WikiActivity wouldn't distrub normal user, and it would help normal user that wonders how do editor works and how active the wikia is by a lot. If they know the wiki is highly maintained, it would encourage them to help there. That is my personal experience.

Long story's short: I wouldn't remove WikiActivity from header for anonymous because it is one way to recruit new editors.