I think much of the general public weren't aware that there already are alternatives to SS for some people, and they are very happy with them. I was listening to a talk radio show last week, and a teacher called in from some mid-American state (can't recall which) where teachers get to put their money into a low-risk, carefully-regulated private pension fund instead of SS. She said people there become teachers because even though the pay isn't great, "you retire rich."
I've got some family members who are teachers--and what you're describing sounds like how their private pension system works. I don't think that's where they put any part of their FICA taxes though. This is in Indiana though. Maybe in some other mid-western state??