IF they're worried about abuse, the delete button could be more of a "hide" button.
That way the post (or even just the content of the post) isn't normally viewable except by forums staffers, so it remains for posterity and review, if there is a case of abuse.

I'm not sure how well it would work out for the mods, but it could also flag the post when you do that and alert a mod the post needs to be reviewed for permanent deletion. Maybe a multiple choice option for the "reason of deletion" could be added? [Duplicate Post, Wrong Thread, and things like that.] So they could be categorized.

That way you could have the self moderation and keep the post from interrupting the thread with unnecessary content, and the content could be deleted at the staff's discretion.

It sounds nice, but I'm not sure how easy it would be to implement something like that though