I've observed no few edits being made because the commenter realized that they'd said something that they maybe didn't mind me knowing or would have said to me in a more private forum, but that contained information that didn't need to be shared with the whole internet.

Leaving the old version up would be enough of a change to expected behavior that if this happened, there should be something explaining what would happen on the edit screen.

Someone who's not okay with having the old version remain up would still be able to do the poor user's edit, the delete-and-repost.