You pose two separate issues here.
One in your title which is "Should SO be more restrictive with new user account creation?" I think that the current amount of work done on the Stack Overflow team side has been great. The email banning process seems complicated and that is also an issue with the use of the OpenID system in general. I am not sure there is much more that can be done here.
The other is about barriers to asking questions. I am fairly familiar with these discussions on question quality and restrictions. These are some of the questions I have asked trying to address this topic:
- What effect would introducing a small barrier for new users to ask a question have on Stack Overflow?
- Increase close vote weight for gold tag badge holders
- Make it easier to close job shop "gimme teh codez" questions
- Offer redemption to confused question banned users
- No one likes quitting cold turkey
- New users don't value reputation
I agree that reputation should not be used as a line in the sand barrier. However, that doesn't mean it should be outright ignored.
I propose a rebalancing of barriers towards asking questions through the combined metric of reputation and close votes.
This would essentially be deputizing users to have a stronger impact on new users. It could start small.
- Introduce an additional two close reasons which are only applicable and only available on questions asked by users who have less than 6 reputation at the time of asking.
- Reduce the amount of total close votes required to close questions asked by users who have less than 6 reputation to 2.
- Allow users with gold or silver tag badges to close questions from 1 reputation users with 1 vote.