I deleted an answer. I decided to add a comment to it since the 'add comment' option was still shown. I typed the comment and hit submit; only then did it say "You can't do that". That is not a good user experience. Don't display the 'add comment' option when it cannot be used.
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This only happens if you just deleted the post. If you refresh the page, the link will be gone.
But I agree, the link should be gone regardless.
Actually, it is more instructive (i.e. it teaches people how the system works) to display a link and offer a message explaining why the link cannot be used under certain conditions, than it is to inexplicably display and hide the link in a manner that appears to be random.