Often a question that hits the hot network questions list or otherwise becomes controversial, attracts a lot of low-quality comments. I understand that this puts the moderators in a difficult position, but what I'd like to propose is that once it becomes clear that removing large numbers of comments is needed (beyond one or two problematic commenters), the moderators do so in bulk rather than selectively.
That is, either we should put the Controversial Post mechanic into effect, or there shouldn't be wholesale deletion of relatively normal comments.
I had a highly upvoted and on-topic comment on this answer deleted ostensibly because "it mostly reinforced the answer and being prone to misunderstandings." This is a very weak reason for deleting comments, and I think it should be quite obvious that many other comments on that page have not been deleted even though they too "mostly [reinforce] the answer and [are] prone to misunderstandings."
I'm all in favor of moderators acting aggressively on comments (which aren't a core part of the Q&A format) on controversial questions. I just don't think it makes sense to be really aggressive in deleting some comments but not others. So I'd like to propose that on questions that are protected the moderators go ahead and delete all discussion-y comments.