A simplified, improved and feature-requestified version of this answer -
What if SO required new questions to achieve a net score of +1 before they can be answered in order to improve quality control?
New questions would get a banner to the effect of
Your question is now under peer review. Once it has a net score of +1 votes, it can receive answers.
Once a net +1 has been reached, the question is "unlocked" forever. It doesn't go back into "unanswerable" state if it gets downvoted after unlocking.
Higher-rep users would be able to "rescue" a misunderstood and downvoted question by investing a 50 bounty, which they could do without having to wait 24 hours. Putting a bounty on the question would immediately unlock it and make it answerable.
Questions that are not answerable cannot be searched.
Questions that do not manage to become answerable after a certain time will be automatically deleted.
This is fairly radical, and would make SO feel much less welcoming towards non-perfect questions than it currently still is. But maybe that's a good thing? The only way to really grab an asker by the balls and force them to improve their question is to not provide any answers until it's done.
Voting would get an even more crucial role than it currently has. Voting would have to be encouraged even more.
Voting behaviour would become even more slanted towards upvotes, because an upvote is required to make a question live at all. To me, this is not a good side effect, but the expected advantages still outweigh it.
It would become impossible to answer downvoted questions, something that sometimes makes sense - but in my eyes, so rarely that it's justifiable to lose the possibility. Also, once a question has been unlocked, you can still -1 it after answering it, which is perfectly okay (because the question doesn't go back into "unanswerable" state).
What do you think? I'm not 100% sure whether this would be an improvement, or too much - but as I said in the original contribution, I find this an intriguing idea and definitely worth thinking about.