I delete possibly more comments on a daily basis than most moderators, so I'm going to talk a bit about my experience.
Interpersonal Skills has a very strict comment policy - though, we're merely codifying and enforcing Stack Exchange policy regarding comments. As such, comments are flagged and removed at a rate of about 1000 per month.
There's (at least) one major flaw with your proposal. It's only one-way accountability. You're asking the system to finger a specific moderator (though even if it was merely a generic "moderator" it'd be the same issue) for doing their job without showing the actual content that was removed, which often would make it apparent why it was removed. Without two-way accountability, a lot more accusations of abuse are likely.
I see that there are 20 deleted comments here - why? Moderator X is ruining the community connection on this site by clearing out comments! Y'all get your torches and pitchforks and let's tar and feather them at the stake!
It's one thing for the person who deleted the comment to ask for help understanding why their own comment was deleted or for the OP to ask what the comments they were notified about had said. These users are aware that the comments were removed and if they want to know why, I'm happy to explain...
... but... I see no benefit in responding to idle curiosity that only exists because we have told them in the UI that a bunch of comments were removed. And they will ask. Even if it's not out of concern of moderator abuse, someone who has only ever looked at the post once will see that number and ask "what were the deleted comments here?" or "why are so many comments on this post deleted?". Responding to these curiosity questions takes time away from actual moderation work.
So, we either dupe close them on meta of a generic "why were comments removed" question (if the question was asked on meta and not as a comment on the post), or we ignore them entirely and then risk being accused of ignoring our duties in explaining our actions - which, in this case, comes from users misunderstanding what comments are for (see below).
When I delete 100+ comments from a question (or even just one), I do so for a very good reason, not because I feel like it. Often, in fact, we already post comments saying something like
Seriously, y'all... the answer and joke comments need to stop. We've deleted nearly 80 comments from this question talking about wasting paper, Anne being overbearing, and how infinitesimal the amount of power being wasted is. It's been said already and deleted. Stop it. If your comment is not asking for clarification, say it to yourself and move along.
Though more often that not it reads something like:
{COMMENTS REMOVED} - If you have an answer, write an answer in the answer field below. Answers written in comments will be removed.
Note, if you visit that question, there are two notice comments telling people not to post answers as comments (including the one I've quoted) plus two explaining commenting policy... and 110 deleted comments.
We're not strict about comments on our meta site as meta is more about discussion.
I'm going to go off on a bit of a tangent because I think this is a concept that not everyone understands...
Why do comments need to be deleted?
Part of what causes this is discussed by Robert Cartaino on this MSE question: Fixing comments in 5 minutes. Intrigued? Let's discuss
The word "comment" is a misnomer for what the intended purpose of this feature is. Comments are specifically designed as a place to ask for clarification or suggest improvement. In Robert's words:
Comments are something else. We have a section inviting folks to simply "add comment" (definition: respond? gossip? talk?), and yet we yell at them if they do it wrong. Then we spend an inordinate amount of time (and resources) cleaning them up (with barely a dent, I should add).
Comments actually have two primary use cases — to ask for clarification or to suggest improvements to a post.
This is made clear in the comment use privilege explanation page on any site:
When should I comment?
You should submit a comment if you want to:
- Request clarification from the author;
- Leave constructive criticism that guides the author in improving the post;
- Add relevant but minor or transient information to a post (e.g. a link to a related question, or an alert to the author that the question has been updated).
When shouldn't I comment?
Comments are not recommended for any of the following:
- Suggesting corrections that don't fundamentally change the meaning of the post; instead, make or suggest an edit;
- Answering a question or providing an alternate solution to an existing answer; instead, post an actual answer (or edit to expand an existing one);
- Compliments which do not add new information ("+1, great answer!"); instead, up-vote it and pay it forward;
- Criticisms which do not add anything constructive ("-1, see previous comments you scallywag!"); instead, down-vote (and provide or up-vote a better answer if appropriate);
- Secondary discussion or debating a controversial point; please use chat instead;
- Discussion of community behavior or site policies; please use meta instead.
Note that the second point in the "When should I comment" section may be a bit confusing... this is the "suggest improvements" part. These suggestions for improvement shouldn't turn into a multi-comment discussion/argument between users... if they do, it should be taken to chat or removed if it's not serving any benefit as mentioned in the "When shouldn't I comment" section.
So, because users think that a "comment" is "anything that comes to mind in relation to this post", they frequently feel that any removal of comments is unwarranted. In fact, the opposite is true.
Comments are for such a specific purpose that a very low percentage of them actually belong on the site and once acted upon, even those comments should be removed. Comments are noise and the more of them there are, the more there is coming between the person who has a question (not only the OP) and the solution to their problem.
This is particularly problematic when the comments appear on the question, as they appear before the answers. Add to this the fact that comments can only be voted up, you are treading in dangerous water of bad advice that merely sounds good to some people (who have upvoted the comment).
So, my argument is
Until people are actually using comments for their intended purpose (or understand that purpose), all that something like this will do is cause annoyance to moderators who have to deal with accusations of "mod abuse" for deleting comments the user may never have seen.
The inevitable answer to "why was this comment deleted" is nearly always "because it was noise".