You're forgetting about private pension funds. Those are massive, and often mandated by a collective bargaining agreement.
For comparison. France’s pension funds (total public and private) are 12% of their GDP. Total EU pension funds are also around 20% of total EU GDP. USA pension funds are 170% of their GDP!!!
Yes, we have a pays-as-you-go pension system in Denmark (sigh). But regulations were also changed a while back such that employees must pay into a pension scheme of their own. In our case, that's handled via your employer and there's a minimum contribution limit and often incentives to pay a higher level.
((not my area of expertise))