There's not much social cost to harassing someone within the limits of the law. Or even just outside the limits, since police rarely are willing/able to do much about online misdemeanors.
Well, you can ban the person - and I would believe that some people's vitriol would substantially decrease if they had their names tagged on a particularly hateful statement. And if these Real Names were consistently kept accurate, wouldn't it be easier to sift through and ban offenders?
Yes, but this only affects people's online activities. It additionally forces otherwise innocent people to open themselves up to offline, real-life harassment.