Often there are discussions between two or three people in comments - and most are finished without moving or simply become obsolete quickly due to edits in the answer/question.
Of course one could now delete the now-useless comments but with replies from other people it would become pretty confusing. An easy way to avoid this would be the possibility to mark a group of comments for atomic deletion. Unlike the current comment flagging system this should only have one reason, "obsolete", and high-rep people should see those flags so they are likely to vote for/against deletion of the discussion.
Instead of creating a public vote it could also be done in a way that it is only shown to the people involved (i.e. the authors of the comments) and only one of them can suggest such a deletion. With all authors agreeing these comments would automatically be deleted.