The fact that there is no quote feature is the very reason that allowing someone to delete their own posts works. It wouldn't really be "deleting" your post if your message remained in a later response.
Keeping replies would be due to the fact that a poster owns his own posts so the person removing HIS own post has no right to remove that of the person responding plus the response may well contain useful information in and of itself.
One suggestion I'd make would be to specify whether an edit is made by the poster or the board admin--I notice that messages I where I edited surnames as admin months ago reflect that the surnames were edited but don't specify that the edit was made by the admin. Perhaps if the posts did indicate this fact it might serve as a learning tool for the poster in how to properly use the surname box.