What about if instead of restricting user registrations, you treat questions by unproven users differently?
Put them in a separate bucket and treat them as 2nd class questions until one of the following happens :
- They get upvoted
- They get an answer that is upvoted (by someone other than the OP?)
- OP hits a specific rep milestone
These second class questions would get treated differently :
- Are ranked lower in Google Searches (can we do this?)
- Can be filtered by users who don't want to see them
- Are excluded from "hot" lists
- Possibly ranked lower on the Home page
- On track to be Roomba'd and deleted
Keep in mind this is only for questions posted by users who have not proven they can ask a decent question or that they understand the site. Once they get some rep, their questions would be treated the same as any other.
I've seen ideas like this in the past, and some of the concerns are
Nobody will monitor the 2nd class questions
Now personally, I don't mind beginner, or even bad questions. I just like helping people, pointing them in the right direction or guiding them to ask better questions. Back when I was actively going for rep, these were some of the only questions I could answer because I either didn't know enough, or wasn't fast enough. I don't see this as being a problem.
New questions need visibility
They'll still exist in the question lists for most users. Filtering them out will be an opt-in thing for users that care about this kind of thing. For most users who don't know/care, or those who like seeing all questions, or rep hunting, or who just like helping people, we'll still see them.
It will be too easy to gain rep in low quality questions
Rep is just a measure of activity, not necessarily excellence. In my opinion, people who are active on this site helping others deserve rep. Those who stick around for any amount of time will learn the site rules and eventually grow to help more then they hurt, and potentially be the high-rep users of tomorrow. And if you're really that concerned, scale the rep games for 2nd class questions.
We don't want to drive away "experts" by treating them as nooblords
If you can ask a decent question, it will usually get upvoted, especially if users are aware of how 2nd class questions work. There are many of us that just like to answer questions, and don't care how the site is run as long as it doesn't impact our ability to help people, and we will not be filtering out newbie questions. I'm sure we've all seen high rep users post answers to "bad" questions to prove that.
TLDR: Sometimes its much easier to allow everything and filter it, than it is to try to create restrictions and unnecessary hurdles that can drive away good users and content.