There is no reason they cannot, other than it costs. And if the "little guy" can manually moderate a forum, and respond to unblock requests, then it is no problem for Facebook, or any other big player too.
In truth, Facebook would still save over "the little guy's" moderation methods, as Facebook has the size and scope to develop software tools to significantly improve the workflow of manual moderators.
All this "but it is impossible!" blather I hear, re: manual moderation just means "cause our profits would drop a little".
Oh boo hoo! Manual moderation is the future.