I think it's important to emphasize that much of the in/out money asymmetry in SS is not rich versus poor ... but old versus dead.

Which, incidentally, is good and proper! OASDI is an insurance policy to cover an (alive) person faced with starvation or living in a ditch. That's a very different set of tradeoffs from an investment account that can pass to children who don't need it.

Like all insurance, it depends on a portion of people who pay in and then don't need it, even if sometimes that's because they've, er, passed beyond all material needs.