To me fizzbuzz eliminates certain types of candidates who have absolutely no reasoning skills. You would be surprised at how many people are out there who have learned how to regurgitate lessons from school but seemingly have no clue how to solve any real work.

These people do manage to get themselves hired based on their academic degree and they wind up contributing absolutely nothing, while consuming time from the developers around them until eventually they are dismissed.

You don't want one of these guys on your team. Simple fizzbuzz exercises will usually uncover them unless they have managed to memorize it previously.