I only come to Academia occasionally, but I moderate on another SE site.
I think moderators have the right to edit comments in a way that they deem best for the site, and I don't think they should be handcuffed into making a group decision before deleting a comment. The Stack Exchange is pretty clear on this one: answers are permanent, comments are temporarytemporary.
When I'm moderating, I treat each situation as its own case. Sometimes I'll delete an obsolete conversation, sometimes I'll leave it as a helpful guide for new users. (Comments explaining why a question was closed might help new users learn more about the standards for a site, even when there's some disagreement and debate among regulars.) Sometimes I'll leave part of the conversation there, and trim the excess. Every once in a while, I'll combine two comments into one.
Overall, occasional deletion of comments is healthy for the site, particularly when they become too "chatty," too distracting, too hostile, too lengthy, too sidetracked, or unconstructive. Of course, everyone has their own dividing line. One man's trash is another man's treasure (or, as George Carlin once remarked, "Ever noticed that anybody driving slower than you is an idiot, and anyone going faster than you is a maniac?"). The crowd doesn't always agree with the umpire behind home plate, but the game would take forever if everyone had to vote on each pitch. In the same way, some moderator decisions won't please everyone.
In short, I try to do what's best for the site as a whole. My vote would be for that to be the prevailing guidance: let the moderators do their job, and don't make mountains out of molehills when comments get deleted.