How about deleting the questions which are not welcome to be entertained?
Some questions are closed as not constructive even when it has many upvotes - which means, people like them.
Some questions are closed as not constructive and also has down votes - which means, people do not like them.
In either case, "Closing a question" (not protected - closed) - indirectly means - You're not allowed to answer because this question is not welcome here.
Considering that we want to keep users happy, we may rule out deleting it completely for point 1 but, "I do not see" any apparent reason to keep questions, like those mentioned in point 2.
My point is, how about implementing a feature of 'deleting' the posts with 10 downvotes instead of keeping them?
It's like recruiting an employee to show company strength (be there on Google), irrespective of his productivity (of it being closed).