Should Stack Overflow be more restrictive about new user registrations?
We seem to be shooting down most suggestions that intend to have the net effect of throttling new questions. I'm attempting to list the canonical suggestions and reasons they are being shot-down or at least the questions that are being raised.
The principle here is that given a random (genuinely) new user, we want to immediately accept their input.
This is an important principle. In short, it's a "No" to your main question.
But the problem the question is getting at is the problem of too many bad new questions, and an inability for Stack Overflow to handle them all.
Principles
First, here I enumerate principles that are guiding this discussion:
Given a random (genuinely) new user, we want to immediately accept their input.
This site was created in part in response to the way Experts-Exchange behaved. It would be a departure in strategy and offend many pre-existing users if we act like they do.
Bad-faith users will do whatever they can to get around roadblocks for posting, so we have to align incentives so that they don't create problems in other areas.
"We don't want to spend a lot of effort developing something that might not work." I think this is probably a really bad principle, and investors in Stack Overflow would probably not be happy with it. You have to weight risk as a cost in making a decision on the capital expenditure.
Don't make the innocent suffer. I think this is fine unless it prioritizes new askers over answerers. Remember, innocent answerers are suffering from all the bad questions.
Given a bad question, if we can fix it (remove the badness) and answer it (not necessarily in that order) then we should.
Other's Suggestions
So in the context of the principles, I'll address the suggestions:
Two-Factor Authentication: Will young users or people in the developing world be able to authenticate? See principle 1 as well.
Impose time delay between account creation and ability to ask a question: No - see principle 1.
Test new accounts (programming or even IQ testing): See principle 1.
Charging $1 to create an account: see principle 2. Also they would act even more entitled - they paid after all.
Minimum reputation points to ask: See principles 1 and 3.
Penalize answerers of bad questions: See principle 6 but also we can downvote such answerers if we think they are behaving egregiously.
Question Wizard: I think this can be tuned so that it makes it harder to get around without violating principle 3. It violates principle 4, but I think that's a bad principle anyway.
Review before going live on the front page: See principle 4, likely not an easy modification to the site. Also, this is a marginal violation of principle 1. However, this is approximately what Hacker News and Reddit does with their "New" sections, their "front page" is essentially "Hot Network Questions", and I don't think they get a lot of complaints.
Suggestions:
In light of the above analysis, here's my suggestions, in multiple parts:
Suggestion to Users
If you see a bad question, and you can fix and answer it, then do so. If it's bad and unfixable, and further, if you think an answerer was wrong to answer, you can downvote the answer as well. If you were right and it's all deleted, you regain your rep point you spent on the downvote anyways.
Suggestion to Stack Overflow
Let's explore 2 factor authentication as a way to accelerate the rate at which we trust new users. Multiple contact points may encourage better behavior because real world reputation would be more in minds of those who authenticate at a higher lever. However, I'm against making it mandatory for the present.
Give askers a better interface to guide them away from pitfalls and keeps them on-topic to the site.
Give answerers a better set of screens. Allow them to create their own ranking algorithms that can give different weights to recency and upvotes (within certain tunable parameters such that this is not a burden on the server-side). Thus answerers who want to see questions from new accounts can see them and those who want to limit their view to better questions could do so.