Do you think people should be allowed to delete their question?

You know how after someone answers on a question, you are unable to delete it and need to report it to take it down? Do you think that option should be allowed? The other day, I saw an user asking people to stop responding to their question since they thought they made it anonymously. The question got a lot of criticism since they made it on an illegal site like here. Won't this follow them around forever?