If she called law enforcement every time she got a threatening tweet or email, there's a good chance the cops would stop taking her seriously. They only have so many man-hours to dedicate to investigations like this, and each one takes a while. In the mean time, she's still subject to more abuse which strains her mental health even more. I wouldn't discount the possibility of serious self-harm in cases like these.
While it would be nice if there were a streamlined process to report threats like these to the police, and a streamlined process for the police to investigate them, there's a more important action here: protecting innocent people. Twitter has the means and ability, and in my view should be a moral imperative, to keep people from harm if they can help it. Twitter can do more to protect people from hate speech and abusive language, which would greatly reduce the suffering of many people.
We don't have to hold Twitter responsible for how their users treat others, but we do have to hold Twitter responsible for how they treat their users - which is to enable their abuse by other users. Can you imagine if ten Starbucks customers were verbally abusing one woman and the Starbucks employees did nothing? At the very least, Starbucks should be expected to call the police on behalf of the victim, just as Twitter should do. Sadly, we don't hold social media companies to the same moral standards as a coffee shop.