The current rate of savings of the American public is slightly under 1.8% of gross earnings. Simply put, the average American household of 4, two adults, two children, earning $50K per year will only save on their own, $900.00 annually. Their average credit card debt is $8000.
Most people don't know the difference between a load and no-load fund, a stock, a warrant, an option, a bond, a certificate of deposit.
The system of privatization will not be optional. It's too difficult to service and maintain, if everyone isn't in the system. It'll necessitate a corporation like FDIC to insure against losses. That will require contributions from everyone.
If there is partial privatization, two things will happen immediately. Both employer and employee contributions will rise above 6.5% and the $90K cap on FICA assessed earning will rise to $140K or higher.