If there are a large number of comments then when they are rolled up only (some of) the up-voted ones are shown until you hit the "Add comment" link. Therefore if we respond to a "more than 20 comments posted" flag by adding a comment along the lines:
Can any of these comments be usefully incorporated into the post? If not please take the discussion to [chat]
This comment is not immediately visible and only becomes so it it has a lot of up-votes.
For example - see this question on Programmers. The system generated the "more than 20 comments posted" message and I added a comment along the lines of the one above. Even though it's been upvoted it's still not visible on the default view. Having it visible would act as a deterrent to people adding more noise.
Initially I thought it would be really useful if we moderators could "pin" such comments so that they were always visible - but I don't think a general purpose solution which only has limited use is required. We already have the ability to add post notices, so:
I'd like to request a new post notice option for this situation.
Alternatively add the ability to prevent comments being added (time limited of course) with a system message telling people to either incorporate the comments into the post or take the conversation to chat.