I don't understand why people wouldn't allow deleting posts. phpBB only allows non-Moderators to delete their posts if the post is the last one in the topic.
The only problem with the phpBB deletion policy is that somebody could be quoting your post when you delete it, and if the quoter hasn't submitted the post when you delete it, their submission will include a quote of a post that's no longer there. Presumably that's a rare case, but it could happen. Even worse would be if they didn't even quote the post and just referenced things in it (something that's often done when replying to the last post in a topic), so there's not even a quote in the reply for context. (That's one reason to always quote the post, even if it's the last one. Another is that somebody else could post between the last post and yours.)
One example where allowing deletion is useful is duplicate posts. If I had accidentally posted a duplicate, I'd want to be able to delete one of them. Yes, moderators could do it, but I might notice it well before any moderators.
As an aside, here at phpBB.com, they don't seem to delete lots of posts that probably should be deleted. If somebody posts a duplicate topic, a topic that violates the rules (like recruiting), etc., they tend to just lock the topic instead of deleting it. I still don't understand why. Do they think those topics serve as examples of what not to do?
(I do know that some posts get moved into a hidden forum, but there are still lots of locked topics that probably shouldn't be there.)