Suicide-baiting works because no one likes the idea of being responsible for someone else's death. That's why you go nuclear and call the cops once the suicide-baiting starts. It's just one more bargaining chip narcissists and attention whores like to use when things aren't going their way, so you take it away from them, with prejudice. You don't bargain, you don't urge them to get help, you don't do anything except alert the authorities and let their dumb ass deal with a 24-48 hour psych hold for throwing a temper tantrum. It has nothing to do with white knighting and everything to do with retribution for being a manipulative fuck.
Of course, it usually works better in person, or if you have doxx on the internet commenter threatening it, but whatever.
