First of all, the premise isn’t totally true. We’ve talked a lot about Gabby Giffords. And Kitty Genovese is a famous name while I’ll bet you couldn’t tell me who raped and killed her.
There’s good reason to focus more on the perpetrator. For one, not everyone wants to be publicly scrutinized, and we’re more solicitous of victims’ privacy because they didn’t choose to become involved in the crime. If we try to get a well-rounded view of the whole person, we might find out unsavory things like that the victim has a criminal record, which will (unfairly) cause some people to care less about the crime. We could find out salacious details about their family or love life. If the crime is a major story, it’s inevitable that some contrarians will try to make the case that the victim sort of deserved it, or brought it on themselves, or was as bad as the perpetrator, etc.
Could media get around those problems by not reporting on victims with checkered pasts, and focusing only on victims who seem to have led exemplary lives? Not really. For one, you can’t make sure no one blames the victim even if the victim is known to be a saint. Also, the victim might appear completely admirable by the time the reporter’s deadline comes up, but negative facts about the victim might come to light later on. And on top of that, the media should be in the business of reporting objective facts based on some consistent principles and policies, not cherry-picking facts that will make us feel good.
Aside from all those problems, the victims of, say, a mass shooting are likely to be a random cross-section of the public. That can actually be interesting, e.g. the New York Times released a book of profiles of those who died on September 11, but as a general rule finding out details of these people won’t be any more informative than reading about any other group of randomly chosen citizens. In contrast, the shooter is more interesting simply by being more unusual, and learning more facts about the person could lead to insights about issues like crime, guns, etc.