This is actually messing with notifications as well. I have not tested this recently but I believe that if you subscribe to the discussion you can entirely miss posts that were stuck in approval if new posts were added in the meantime. This means even if you keep up and mark the discussion read each time you get a notification (so you get the next notification), you will still never get any notification for the post that was under approval.
And just generally, if multiple pages of new posts are added in the meantime, you might never notice a new post that appeared earlier in the timeline during regular browsing.
At the same time, there are also use cases where the original post date is important, so I don't think just updating the post date to the approval time will result in an improvement for every forum.
In my still unreleased album extension, I dealt with this by having 2 different values, the upload date and the publishing date. The publishing date is only updated once a picture is out of draft mode and has been approved by moderators. Maybe we should have something similar to reflect the date at which the post became public, and possibly sort by that attribute first.
Then there's the whole mess of post numbers. I believe posts under approval already get assigned a number, so if we re-order them based on publish date the numbers will be out of order. Maybe there could be a way to keep the post on hold and only assign a number during publish, at which point it would match with the order we want posts to appear in.
Maybe another use case worth mentioning. On this forum I think we semi-regularly reply to discussions still under approval under the Extensions tag for example, to ask the user to add information before we publish the discussion. If the whole discussion is under approval we should make sure to keep the existing order of all posts already in the discussion, most notably make sure the first post stays the first post even with a moderator reply in the discussion that never went through approval.