When you post a link that's already been posted, a "dupes" section will pop up letting you know it's already been posted. Pick any link on the homepage and put it in the link form - you'll be able to see what it looks like.
Sometimes there's an accidental reply I made (e.g., replying on wrong SN post), or a Post that I make and then see shortly after someone else posts on the same time, or for whatever reason I wish to "undo" my post.
Could there be a short window to allow delete? Sure, if there are replies to my post , or replies to my comment, then no -- restricting delete in that instance makes sense. But if it is new (e.g., ten minutes, or two minutes even, whatever), and has no replies, not upvotes, etc., can't Delete be allowed?
Why couldn't it show up during the edit window? I don't think it goes against anything - yea, people may already tipped you some sats, but they presumably got the value from the post already, so that's a fair game.