There is an specific reason to disallow that a closed question be deleted by his owner? I mean, if the question is closed and it doesn't reach the forum rules, why the owner can't delete it if he wants?
You can actually...
As long as it's your post, and is at least two days old AND there are not upvoted answers.
But in order to delete other's questions you need 10k rep. If you look at your privileges page and select 'access to moderators tools' you'll see a reason why deleting ALL questions that are already closed is discuraged:
Before voting to delete, please check that there are no good answers -- if so, then the question should be flagged for moderator attention as a potential merge candidate. We don't like to lose great answers! Also, be cautious when deleting questions closed as duplicates - if they can serve as a signpost, directing users to useful answers on another question, leave them be.
I would say that if you want to delete a question, first contact or flag a mod first and let them handle the question and answers.