I just had a discussion about that very thing with friends. I think it's because the case is essentially a murder mystery, and everyone loves a mystery. I don't think that it's because she happened to be from a wealthy family--there have been highly-publicized murders that had poor or middle-class victims. At least that's not why the case fascinates me. The reason I follow this case is because I've always been interested in criminology and especially profiling, and I find the minutae of this case very compelling.
My friends were somewhat combative. Their opinion seemed to be, "she was rich, so who cares that she died?" Or, "why are so many people mourning her? If you're going to cry for one of these things, you have to cry for them all and we don't have the energy." One even had the gall to say "I know she would have grown up to be a b#tch. Do we really need another one of those in the world?" and I really let him have it for that. Regardless of how you feel about this whole mess, that is an absolutely disgusting thing to say.
I'm sorry if I sound defensive, but I have to ask: Why is it "wrong" to care about or be interested in this? And I don't mean to say that you, DG, are saying this; that's just a common perception I've been getting from some people like my friends and I don't get it.
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