Why does MySQL allow "group by" queries WITHOUT aggregate functions?

According to this page (the 5.0 online manual), it's for better performance and user convenience.

I believe that it was to handle the case where grouping by one field would imply other fields are also being grouped:

SELECT user.id, user.name, COUNT(post.*) AS posts 
FROM user 
  LEFT OUTER JOIN post ON post.owner_id=user.id 
GROUP BY user.id

In this case the user.name will always be unique per user.id, so there is convenience in not requiring the user.name in the GROUP BY clause (although, as you say, there is definite scope for problems)