Furthermore -- and this to my mind would be the single biggest problem with immortality (a concept I still think is a pipe dream) -- most people's and ideas and worldview tend to crystallize at a certain point, and never really change after that. Death and the emergence of a new generation are a natural check; each new generation realizes in a different manner some facet of what it means to be human. With immortality, we would likely see stagnation, with the world run by people whose ideas matched material reality three or four hundred years ago. Think of tradition in the very worst sense, as a "dead weight" which current humanity is trapped under; and now imagine that tradition still living and enforced by the actual people who created it.
To me, that line from How the Steel Was Tempered is the complete expression of communist morality and a truly human attitude toward death: "The most precious thing a man possesses is his life. It is given once, and never given again. And it should be spent so that in dying, one can say: I gave it all, my whole life, my whole strength, for the greatest thing that there is -- the fight for the liberation of humanity."