Currently I think many of the Not an Answer or Very Low quality flags we see should have been some other flag, but we do not have that flag. This flag would give us that other option.
This would be good for the answers that are I think you should do X type of answer, or I think you are being treated unfairly, etc. Many times the sympathy is widely shared so the answers get voted up despite the fact that they do not provide a quality answer that is going to be useful in the future.
It would also give us a mechanism for clearing out answers to questions that were asking for the opinions when posed, but could be made constructive if not for the answers that already exist.
The flags would still just be for alerting the moderator of the need for action, but perhaps if we get to a certian threshold for the flags it could automatically trigger the back it up blurb that moderators can current set.