I think that comment-cleanup should be encouraged by adding comment noise as a predefined reason for flagging content for moderator attention for multiple comments that are made irrelevant after a question or answer has been updated (e.g., after a clarification).
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Sub reasons are for the most common scenarios that really need to be addressed - close reason, non-answers, and low quality. Huge comment cleanups don't happen all too often, so as Robert notes you should just enter the comment noise into the textbox for the flag.
Moderators probably have better uses for their time.
If you're bored, flag the comments themselves. If others agree, they can flag too, and the system will remove them. If a moderator is bored, they can whack the lot. Most likely though, no one cares.
It is expected that comments have a slightly lower signal to noise ratio than questions and answers. Currently, at least half of all comment flags mark something as spam or offensive when in reality they just express a technical disagreement.
I'm worried that another reason for flagging would just result in more comments being flagged that probably should not be, which would lower the signal to noise ratio in the moderation queue. Thanks to the improvements in the flagging system, that ratio is finally starting to improve.
If you see a conversation in comments degenerate into absurdity or burn up in flames, just flag the post in question and add specifics there. Another thing to let us know about are broken conversations that lost their context due to the system automatically removing comments that received a lot of subsequent replies due to flags.