Learn the fucking laws people, and I mean you too police officers, and fucking use them properly.
While I agree with your statement in full, it belies the problem. You see, law enforcement has not caught up with the ease of harassing people online.
1) Most police units are barely aware of online activity past trying to catch people boasting on Facebook about breaking the law.
2) Even if they were aware, most don't see this harassment as more than some form of bullying (and most adults don't see bullying as anywhere near the huge problem it really is)
3) If they are aware and see it as a real, law-related problem, they probably have no funds to pursue it
4) If they have funds to pursue it, they need to be able to identify the perp
5) In most cases the harasser, the site(s) where s/he does most of the harassing, or both are in another jurisdiction. Now their legal system has to be involved.
6) GOTO 1
This ignores the barriers to getting the identity of the harasser, even if you can get the site to cooperate (unlikely without a subpoena/warrant, unlikely without cooperation from their area's law enforcement, etc.) such as tor, throw-away accounts, and proxies. I fully agree that existing laws can be used against these kind of horrible people, but only if those existing laws actually apply to that person and you jump through a number of other hoops (and pursuing even one of the harassers will likely make the others up their antics.)
Even a civil suit would be incredibly hard, because you have to have the money to hire a P.I. to get that information, then still go through juridstictions. I don't know if restraining orders even hold across state lines, or how you would set them up (the accused has to stay at least 10 hops away? Cannot maintain an account on another website held by the protected?)
Taking legal action against the nastier harassers (like the person who called in the shooting threat when Anita Sarkeesian was going to give a speech) would likely help a great deal. A lot of these kind of people get power from their pseudo-anonymity, so the threat of removing the mask will scare many of them off. But this success would require cooperation on a national if not international level, with the likes of the FBI or Interpol spending considerable time and money for even just a few.
Fucking anti not nice to be law bullshit.
Ah, but politicians! Politicians don't actually care about doing anything, they only care about the appearance of doing something. Raise taxes and/or retask law enforcement efforts to go after online harassers? You'd have all sorts of people calling for their heads in an instant, saying it's a waste of resources that will give little reward that requires tremendous effort. Now, laws... laws are easy and relatively cheap. You make some new law/bill, give it a cute name ("NONETBULLY Act of 2014"), and write overly-broad definitions and penalties that would get struck down quickly when challenged in court, but give the people the idea that something has been done. So you get overwhelming bi-partisan support because it also distracts from any more local and tangible problems and, boom, you get to hit the campaign trails declaring you took a "firm" stance against online harassment.
And, in the end, all the bill actually did was fund a number of riders: the park has a new bird bath, the library on fifth was renamed to Steve Irwin Memorial Library, Barbara down in the cafeteria is recognized for Best Sloppy Joes of the 20-Aughts, and some corn farmers get an extra bump in their water subsidy. Effect on curbing online harassment: none.