Stratton Oakmont v Prodigy Services is only tenuously related to your gripe about websites removing content. Stratton didn't sue Prodigy for taking down posts by Stratton. They sued Prodigy for not taking down allegedly defamatory posts by users.
I asked you to provide a cause of action for "censorship" by a web site. SOvP isn't that. A more recent, federal, and better-fitting case would be PragerU vs. YouTube. There, PragerU sued over their content being remove/restricted. They lost on 230 grounds. But even without 230, they almost certainly would have lost on 1A grounds, because YouTube's exercise of editorial discretion about what content they host is clearly 1A protected activity.
Going back to Stratton Oakmont for a moment: I understand the argument that, absent the liability shield in 230, content moderation of less-than-clearly-illegal content would be vanishingly rare. Web sites would seek to avoid potential liability by getting out of the content-moderation business, which would fix your issue. I'm not convinced that would actually be the outcome. Even if it were, I wouldn't enjoy every web site devolving into 4chan-but-covered-in-spam.