I'm with you on the dubious value of auto-dredged-up questions. If I owned the universe, that whole front page queue would be gone. That includes the queuing of things just because they were recently edited (which the difference between the front page and the "Questions" new stuff only page is, AFAICT, the presence of recently edited + Community dredged questions).
What I'd replace it with would be a new queue proper (as, like the review ones where it takes five votes to close a question) for things that are potentially to be injected into the front page. That could auto-include things that have been recently edited and Community dredged stuff, but there would also an option (with a rep bar, like close and delete voting) for users to nominate an older question for injection.1 This way nothing except new questions would make it to the front page without being looked at and approved by a person (usually at least several people).
What, if anything, can we here in RPI do to move questions like this toward the "purge" bin?
The obvious things are vote to close and vote to delete. Note that (the details here are from memory so may be flawed) closed questions with no upvoted or accepted answer, and (?) no positive score on the question itself, are reaped regularly by the system, meaning it goes from closed to deleted. So in many context close voting initiates that process.
I don't actually look at the close queue for reasons I've explained here before, namely that I'd rather see something go down with 5 community votes than 1 mod hammer. There is a bit of an issue here in that we don't have a large number of regulars with the rep to close vote.2
I do close things all the time, but again, I don't even look at the close queue. I may start to do that with an eye out for this stuff.
There's also flagging. If you flag something "in need of moderator intervention" and indicate you think it is driftwood, if I agree I will close or delete it. You can flag closed questions too, in which case the suggestion would be to delete it completely (which as mentioned above the system often does with old, closed, pointless junk).
Which might be redundant if all it takes is an edit, but never mind the nitty-gritty.
Right now there's 50 3000+ members (after 7+ years). I doubt more than a fraction of those look at the review queues regularly. This is a corollary to the community's stinginess with upvoting, which also helps to create scenarios where we have perfectly good, even exceptionally presented, questions that have the same rough metrics as total crap:
0, which perhaps shadows the problem from question here...