Speaking as someone who has admin'd large forums and been a user on plenty, I'm very against this. The potential for a user to make aggressive or drama-mongering threads, then delete them before staff ever see the contents, are... uh, well they exist lol
If you need a thread deleted, you can always mark it as (Delete please) or even report/link it to staff and request for the removal of it.
I guess a compromise could be an option to "Request Deletion" button on threads, which then hides the thread temporarily while the staff review your request. That way if someone is trying to use the delete option as a means of causing Problems, they... well, can't. The staff would need to approve and finalize thread deletion. :B