That's because for one the net contribution is what is deducted from your check currently PLUS an equal amount from the employer which is the way SS works now. So the worker would never see a difference in take home.
What you fail to grasp is with 40 years of compound interest you turn the roughly 100k into something between 600k and the 980L I saw published.
Compound Interest calculator
The employer/employee contribution is just about $50.00 per week, which equals 2080 weeks of a net of $104,000.00 If we compound that at 4% we get a number of around $300,000.00 or roughly three times the amount of the value of the current SS account since the Government doesn't pay interest.
In order to get a to 7 figures you need a 9% return which means stocks and such. It also assumes you never get a raise. So let's go back to the risk/reward factor. Even if the min wage earner were to have his savings take a 35% "Hit" due to recession they would still have $195,000 in their account which is still more than under the current system.
This is the Legacy of FDR and his necktie Salesman Vice President. FDR screwed several generations by making them dependent not upon themselves but upon a Federal Government that is both fiscally and morally bankrupt. The Federal Government makes the whore of Babylon look Christ like.