>it would be manadatory retirement savings accounts for all and invested in (vanguard) index funds (and probably diversified into bonds at least)

Doesn't Australia's superannuation work something like this? If I understand it correctly, a chunk of your salary is set aside, but instead of going into a pool like Social Security, it goes into a fund. I could be (and probably am) wrong as to how it works. That being said, I would love it if we could implement something like this in the US.