If a question is closed due to being off-topic then it should be deleted, because it doesn't belong there.
Why is it kept there in closed state when it has been established already that it's in the wrong place and no one is allowed to contribute?
That defeats the purpose of trying to maintain the high quality of content of site. Be it closed or open. As long as it's there it's still part of the content.
Ideally, off-topic closures (as well as most non-dupe closures) should get deleted. The reason they're not immediately deleted is because sometimes they can be fixed to no longer be off-topic. Closing's purpose includes given the author, or other users, the opportunity to fix an unacceptable question and consequently get it reopened. That's why they stick around. How long they stick around is dependent on who is running around performing the necessary deletions.
At least in theory, closed off-topic questions serve as a signpost for future posters and show what questions aren't accepted. There are sometimes comments on those questions that add further detail into why the question was closed.
Similar questions asked in the future can be closed as duplicates of the original as well.
I believe eventually closed questions get purged, but I'm not entirely sure on when that happens and whether it's an automated process.
Edit: the question can also be re-opened if 5 people (or a moderator) think it was closed for the wrong reasons. Reopening the question is easier than undeleting, as more people have access to a closed question than to a deleted one. While I agree that questions that are clearly off-topic should be removed, I don't think such removal can be reliably done automatically without deleting questions that can be edited (if needed) and reopened.
Us deleters usually delete the off-topic questions once they're past their two day wait period. I always vote to delete the way off-topic questions.
