Well, I like the idea as well. There are lot of Newbies (and other members) who were complaining and blaming Moderators because of their post being deleted. Sometimes, not all deleted posts are done by Moderators, some of them are deleted by the Author of the thread which is a self-moderated topic and I'm sure that's the reason why some of the deleted posts don't have any PMed message saying "A reply of yours, quoted below, was deleted by a Bitcoin Forum moderator.... and so on" to the users but some are really deleted by Moderators without any notice because their posts are included when a thread is deleted.
By granting the Author of a self-moderated thread to leave a comment of why a particular post was deleted will also prevent other members to make repeatedly thread here in Meta asking why their posts were deleted and also will make them realise what they did wrong.
So, it seems like there's nothing bad will happen when this one is applied in the Forum. I'd like to support this one.
But one more thing. I would like to add this.
When a post/reply was deleted. There must be a default message that will tell the user that their post was deleted in this "example thread" by "example member", just like when a moderator deletes a post/reply. The Author can change/modify the default message if they'd like to.
Edit.
>...<
Based on the image you've provided (this one)
What will happen if I choose the "Do Not Delete Message" option and then click the "Delete this message button"?
Edit.
It's just a suggestion. That "Do Not Delete Message" option is unnecessary in this case.
Oh thanks, that enlightened me. I thought it has some special functions.