After some time with the "3 votes to close" working it seems that, overall, this improved the signal to noise ratio.
Non-salvageable questions, do-my-homework requests and "let me google that for you" are closed very quickly, even before some quick answers are posted
I've noticed some premature closures happening even without comments, but some were improved and reopened
It begins to concern me if the closures will continue to avoid the noise: I've seen several examples of deleted questions being closed, deleted and opened again (sometimes minutes or hours later, sometimes it takes 1 day or more).
Auto-detecting that the new question is mostly a copy-paste of the previous one may be harder to implement, but, would it be possible to make the deleted questions visible for everyone? Wouldn't it be a way of detecting the attempt to hide the closure? Even if a new account is created, the question would appear in the searches too.
Worth noting: sometimes the "new" question is actually improved based on the comments and the "delete and ask again" seems just a way to expedite the reopen process (with the problem that the feedback is lost).