To get abusive notifications, doesn't the unfortunate recipient have to follow the abuser first?
Does Twitter really allow anyone to @mention anyone else without the recipients having to confirm it? Or does it in fact notify the recipient with the full text of the comment, so harassers are exploiting the approval mechanism?
If we accept the notion that Twitter resembles a public bulletin board, then unpleasant (and potentially, hate) speech can and will come at anyone, and just like in real life, often the recipient has no methods of recourse other than trying to disregard it -- not making a value judgment whether this is fair, but this is how it actually happens. Blatant threats to life and property can be reported to the authorities, but most real-life verbal harassment cannot be pre-emptively filtered.
On the other hand, if we respect that each user's timeline, notification space, and knowledge graph is controlled by the user, unsolicited, unapproved @mentions are disruptive by nature. But there doesn't seem to be a way in Twitter right now to disable unsolicited @mentions or make them require the mentionee's approval.
So Twitter, by its behavior, seems to take the first stance. Why, then, does any Twitter user have an expectation that abuse targeting them can be limited by the company?
It's great for when you want to talk to celebrities. Unfortunately, oftentimes celebrities don't want to talk to you.