The new users asking terrible questions isn't actually the problem. A question without any upvotes and answers will eventually get roombad. Also, why would someone ask a question if they got no answers?
We shouldn't be more restrictive about new user registrations. Instead, we should discourage people from answering bad questions. This is the actual problem. I often see users with more than 20k reputation answering very low quality questions, instead of closevoting them. Many of these users have a gold tag badge and could dupehammer these questions (as most of them are duplicates).
I think that if a question gets closed and deleted because it's awful (for example when someone dumps a thousand lines of code and says "it's not working, help me pls"), all users who answered that question should be punished. I don't know what the punishment should be exactly, but it could be for example -20 reputation, and even a temporary answer ban if it happens nth time.
Also, we should make it easier to close questions asked by new users. Reducing the amount of close votes needed to close a question asked by a new user to 2 or 3 seems to be a good idea.