Some groups are really dependent on evidence the person is who they say they were - especially parent groups /Mom groups, health groups, where you’re looking for advice or legitimate local socialization / resource information.
Facebook has no way of actually verifying that you are a parent, so I hope nobody is relying on that to provide any sense of security. And my experience with Google+ is that a real-name policy is a woefully naive way of trying to filter out the maniacs; plenty of deranged people have no qualms about having their actions associated with their legal identities.