I have a hypothesis. This phenomenon is similar to spam, i.e. an overwhelming amount of traffic from a busy minority. If that's the case, the solution may be the same: blacklists. I've attempted to implement a primitive Spamhaus for social media, to test this hypothesis, but it's not something that can be done in one's free time.
I wonder if public shaming is a viable option here. Get e-mail threatening rape? Publish said e-mail. Something tells me that a lot of these morons aren't taking great care to anonymize their threats.