Yeah, I agree the whole platform is set up to comment on their content, how does that expand to personal shit or abuse though?
I agree personal abuse isn't nice but half of the platform is made up of people slinging insults at each other. Twice today I saw a well known comedian single someone out calling them a cunt.
I can't support the police getting involved in twitter spats especially when they are cherry picking who they go after. In the case of Kate v Hayden the latter is not without blemish and can certainly give as good as they get.
If things get taken offline as is the case with Caroline Farrow then police intervention is appropriate (though funnily enough they seem a lot less bothered about that). When it's twitter based name calling and back and forth rows then the block button and report system should suffice.
Being offended and having feelings hurt is not nice for anyone but to go down a road of policing meanness is a recipe for disaster (credible threats of harm obvs fall into a different category).