Prior restraint solutions sit very badly with me: there's a reason that "prior restraint on speech" is near or at the top of the list of First Amendment no-nos (yes, the First Amendment applies to US government entities rather than private entities; the lesson is still valuable). It's a gratuitously bad idea to enable the prior restraint feature sitewide and by default. Besides the principle of prior restraint, that has all the hallmarks of being a feature that scales very poorly because it requires human involvement. Requiring human involvement and discretion is the point, so I'm not sure how one could eliminate that. Further, the part of it that say "if a user has a comment in the pending-approval status, they may not post new comments at all," seems very, very likely to have adverse consequences of large scope. People participate in multiple discussions over time and change their minds about them and behave differently in different contexts in response to different prompts. Holding all of their participation hostage to something they've said in the most contentious available context, seems like a great way to exert a chilling effect on participation as a whole.
I strongly, strongly object to and oppose turning on the prior-restraint feature sitewide by default, and especially to the "if a user has a comment in the pending-approval status, they may not post new comments at all" part of the feature.
That said, the history of moderating large discussions, especially in digital media, demonstrates that giving moderators programmatic tools to enforce their judgment is a Good Thing. So if you consider the proposed feature as "Allow moderators to say that any reply to a comment in the tree rooted at Comment Foo, must be human-approved before going live," sounds like a great tool for a moderator to have at their disposal. It is limited in scope and its effects can be judged and known. I think that's a reasonable thing to add, with the caveat that that shouldn't include the "users who have pending comments can't create other comments" part.