I've heard a lot about the distributional effects of social security on the poor/rich, but I haven't heard much about the effects on the dead/alive.
It seems to me that people who are dead lost a lot from paying into social security while they were alive, and those lucky enough to live to an old age gained from their loss. This seems very regressive to me, though I'm not sure if regressive is the right word. This seems like taking from the unfortunate and giving to the fortunate to me.
That lifespan is correlated with richness implies some hidden influence over the distributional effects regarding economic status. One is more likely to live long enough to collect from social security if one is already rich. One is more likely to die before social security can be collected if one is poor.
It doesn't mean social security has overall negative impact, but is suspect this is an important effect that gets missed in the way most people, even economists, talk about it.