It seems to me there are several issues here which are worth unpacking. Even if it is decided that "extreme public embarrassment" is not a suitable subcategory, these thoughts would apply to any black sheep subcategory:
First is the question of "who is embarrassed?" The answer I would think would be "contemporaries of the person." That is, whether or not we ourselves are embarrassed is not an issue. If a couple of lines are confirmed, I have Viking ancestry, and I would find some of their behavior -- sacking, pillaging and carrying off captured women -- quite embarrassing. But that is not the issue.
Second is the question of "who is misbehaving?" It would be inconsistent with WikiTree's privacy policies of including anyone who is living, or probably the parents or even grandparents of living people.
Third, however, is the question, of "how do we know?" That is where the source documentation becomes important, especially on a genealogy site where biography is so important. I would think that if you want to put an "extreme public embarrassment" label on someone, it would be because there is a contemporary source -- a newspaper article in the 1850's, a pamphlet extant in 1640, a poem by a bard in 1100, that proclaims the embarrassing status of the subject. That would eliminate the subjectivity element. Else you have Jack Day slapping the category on all his Vikings because their behavior offends Jack Day -- despite the fact that bards of the time wrote poems declaiming how wonderful they were!