There are a couple ways this is already done.
When a question's score drops to -4 (or below) it is removed from the front pagefront page, and is therefore "hidden" from many/most viewers. In this case the question still exists undeleted, and will be shown if you view questions from another list (e.g., tag-specific lists, other search results, and even the "questions" tab"questions" tab).
Closed (not as a duplicate, and unlocked) questions with non-positive score and no upvoted or accepted answers are automatically removed if they have been "inactive" for 9 days. There are other forms of automatic deletion which are documented in the Meta Stack Exchange deletion faq.
Other than that, users with at least 10K reputation10K reputation can vote to delete closed questions, although you generally have to wait two days before you can do this. The question being very lowly scored will remove this restriction for 20K users20K users, so again downvotes help. Moderators, of course, can delete anything at anytime. In general, I think it is better to have more human input when culling questions, although it does require highly reputationed users to spend time on janitorial tasks.