That's how it works in Sweden though: part of your pension is your own private investments, they aren't taxed as normal investments since you can only withdraw after reaching retirement age, the other part of it is a state pension. Even with this scheme we still got our retirement age risen.
So it seems it doesn't matter if it's public or private, the benefits of improved productivity is not trickling down to workers, a lot more is produced, generating a lot more wealth, and even with private funds we still get shafted because the capital class wants more and more of the pie.
But how much do workers pay towards pensions? In Austria, 20% of personel costs go directly towards pensions, and almost 30% of the entire state budget also goes to pensions on top of that, which is insane.
So it seems it doesn't matter if it's public or private, the benefits of improved productivity is not trickling down to workers, a lot more is produced, generating a lot more wealth, and even with private funds we still get shafted because the capital class wants more and more of the pie.