Closed questions, except for duplicates, are regularly deleted to clean up the site. I've done that often enough myself on the sites where I'm a moderator. But except for some extreme cases, I always try to leave the questions visible for long enough to give the community the opportunity to overturn the decision to close. My rough guideline is at least 12-24 hours for questions that I personally think have no chance of being reopened again. I tend to wait much longer for questions that have reopen votes, a reopening discussion in the comments or are otherwise in a rather grey area.
The question that sparked this post is the following (10k-only):
It's a question type that has been discussed extensively in recent times: identification questions that are not identify-this-game questions. One of the meta posts about that was also linked in a comment on that question. I don't want to argue here whether that question is on-topic or off-topic, but this type of question is at least somewhat controversial.
This question was deleted by one user and a moderator only 14 minutes after it was closed. The question has one reopen vote, though that could have been from the owner of the question.
I can't say whether questions are regularly deleted that quickly on this site as the tools for non-mods are just very limited for deleted questions. But that is somewhat the point of my post, deleting questions very quickly removes them from the view of the community, making a review of the closure nearly impossible.
I'm not saying that no questions should ever be deleted immediately, but I'd reserve that treatment for questions that are so blatantly off-topic that they have absolutely no chance of ever being reopened.