I think that probably works when it’s just a few people, or maybe even a couple dozen. But when you’re getting hundreds or thousands of hate messages sent your way, including (sometimes) death threats/threats of violence, I suspect it’s really difficult to sort through all that junk. I’m guessing that’s why some people just delete all their accounts and start fresh after things calm down. It’s probably easier than going through all the tweets/emails/messages you received and blocking each individual account one by one.
Also, not all of the hate comes from faceless troll accounts. In the case of August Ames, some of the nasty tweets actually came from real people in her industry, along with many fans who saw what was happening and decided to pile on.