(Please note that I am posting a personal observation, and it would be nice if you responded with where you think I've got it wrong instead of simply downvoting. I realize that there may be things that I do not know about, and would appreciate being informed. Note that ridicule and name-calling inform me only as to your level of couth.)
There will always be divisive topics on which people will be tempted to post anonymously because the things that they post in response to these topics might reflect badly upon them. If the Anonymous Monk did not exist, these folks probably wouldn't post; but because it does, there's a route to post anything at all because there's no way that anyone can know who it was.
I have heard the reasons that people want to retain anonymous posting. I will say I understand them but personally view them more as excuses than solid reasons. Many of the reasons that aren't excuses have real technical solutions. For instance, if you're worried about signing in because your credentials might be stolen, then we should get https: working. I've also heard that "signing in takes too long when I want to post a quick response". If the login adds so much time to the total time needed to post, then the login feature is astoundingly slow and needs technical help.
There are technical options that would still permit anonymous posters to post without their being able to misbehave with impunity. The best, in my mind, would be updating nodes to allow the originator to assert "the anonymous user may not reply to this node" and make child nodes in the thread inherit this setting. This alters the posting model to be more like Twitter's - if I don't want you to see your posts, I block you, and you don't get to post on my threads. You may choose to block me in response. If you're the Anonymous Monk, you don't get to block anyone. If someone chooses to block the Anonymous Monk, they may do so; this means that any responders must sign in to post on that person's threads. This makes the situation self-regulating; people who love anonymous replies can have them, people who don't may choose to not have them. If someone doesn't feel like investing in a login to respond to a "no anonymous replies" node, then that is their choice. Every poster controls their environment - except the Anonymous Monk, who, because they have chosen the advantage of anonymity, loses the ability to block comments on their nodes. If a user's nodes automatically inherited their "allow anonymous responses" setting, that would be extra-nice, but I'd settle for checking a "disallow anonymous responses" box.
So in this scenario, everyone wins. The people who dislike anonymous responses don't have to see them; trolls can be banned from one's threads simply by adding them to your block list, and people who prefer the older "anyone can say anything any way they want" can have that to just by leaving some boxes unchecked.
The true lack here at Perlmonks is the will to find a way to make behaving badly difficult and unrewarding, and the empathy to realize that being on the receiving end of it is acutely painful. This is not a technical issue, but a cultural one - and as such, given the culture, is unlikely to change. There's no way for a motivated outsider to contribute a technical step toward preventing abuse of the Anonymous Monk without having been accepted into the site maintenance group - and the likelihood of this happening if someone has expressed dissatisfaction with the social dynamic is low.
This is a technical suggestion; nonetheless, I expect a lot of emotional responses for the reasons I listed.
TL;DR: In a conservative culture, it's practically impossible to effect change.