I think you are exaggerating a bit with how serious it is, since the stalkers' activity is by the nature of the platform publicly visible to anyone who hasn't muted them. Finding who they are for legal proceedings is no less difficult, depending on the user's posts, than it is for the stalker to find the victim offline.
The transparency of this platform certainly of its own, introduces privacy problems, but leaves this issue to the user to manage. The transparency also hurts the power of malicious parties too, and with a working mute button, makes these people more vulnerable to being noticed and vigilantes empowered to work on defusing the threat. This is a more cooperative model, and has many other benefits but for the issue of cyberbullying and stalking, makes such activities potentially very dangerous.