Just as trolls exploit this aspect of privacy to attack people that they likely would not have the courage to in the real world, so too do pedophiles exploit children that they otherwise would not in the real world. Using this same anonymity, con artists, thieves and all varieties of low lives are able to orchestrate their attacks and subvert the societal protections that would obstruct or prevent their attacks in the real world.
I guess it is all about the person and their moral compass, or in some case, the lack there of. I certainly do not believe that this privacy should be removed from the net - actually I strongly support its preservation. This said, I make a habit of only doing or saying things online that I would also do or say in the real world.
I do however feel that when these facets of anonymity are exploited to the degree that a criminal offense is occurring, the douche bags who are crossing the line should be tracked down and handled - i.e. the story in this article of the parents receiving multiple calls from little pricks after their son's suicide - I am pretty sure that can at the least be construed as harassment and should be criminally perused as such.
In this example, you have misguided youths tormenting individuals who are already suffering greatly - these same youths a) would not like this being done to them had their parents or siblings also died (golden rule) and b) likely would not do this without the separation of the web or the phone system our of fear of having their asses kicked, which is sad in itself...