This may be something I'm making up, but I have the feeling that the fame = immortality concept came out of legacy: people wanting to create a family that continues on after themselves (and is rich, powerful, etc). Which makes sense, because then we're talking about a logical extension of the reproductive instinct. But in the modern world even that seems unreachable to me: we're so utterly different from our grandparents that we might as well be aliens, and the same will probably hold true for our own grandchildren.
I guess all that puts me in the Mike Tyson school of thought on legacy: "We're just dead. We're dust. We're absolutely nothing."