One common use is to pass session data between subsections of a site. For example, the user logs into www.example.com, and is still logged in when they head over to store.example.com.
That could be also implemented in my proposed fix by example.com setting the auth cookies. They will continue to be readable by store.example.com.
Sure, it will require a change on the server side, which is a pain. But I can't think of a practical scenario which will be impossible to implement with the proposed fix.
