I made a small modification to how this works.
To prevent accidental deletions and such, moderators can delete threads, but regular users cannot. A regular user may request a moderator delete a thread, in such cases as it's needed to be done.
Currently a regular user can delete that user's own posts, or modify them.
If you modify a post, there's a few minutes grace period in which you can do so without the edit notification appearing, after this because it's assumed the thread has been read by then, the edit notification will appear.