Users with more than 15k reputation can protect questions. I would argue that it doesn't make any sense anymore to keep this privilege since the automatic protection of questions with three deleted answers by new users has been implemented.
Protecting a question has a practically invisible, but still significant drawback: It can prevent good answers from ever being posted by new users. I think that protection is somewhat overused, and that we, the moderators and the community, should be more careful when to apply it.
proactively protecting questions is a stupid idea, and you should never do it even if the system does allow you to do it.
I agree with that, and my personal guideline on when to protect a question fits very well to the automatic protection mechanism, which is after three removed posts from new users.
There might be some exceptions, but in general I would say that we just don't need to protect questions earlier than that. I almost never use my moderator or 15k power to protect questions and would not miss it at all.
I think that the exceptions can be handled by the moderators, though even those should probably try to avoid protecting questions if there isn't a clear record of bad non-answers from new users on that question. There is no need for this as a regular user privilege and it should be removed entirely, or replaced by some other privilege.