A couple of thoughts:

I had the idea of separating new monks as Guest User and only signed in members would have an option of posting as Anonymous Monk.

We could then award a certain number of Anonymous Monk posts to members based on their XP level on a per day/week basis. So for example, if you're at level 5 you would have five Anonymous Monk posts available to you per day/week.

As for Guest posts we could limit those to a certain number per visit (maybe 3). To prevent users from working around this system, if they post those three times as a Guest the number would be deducted from their available Anonymous Monk posts the next time they login.

I don't think this would "fix" Anonymous Monk but maybe by putting a limit on how many times we can post as Anonymous Monk, the handful who abuse it — may — think more carefully about throwing away a post.

I've argued against Anonymous Monk (although not 'banishing' him/her altogether). I do think it plays a valuable part here but maybe with some adjustments it could be made better.