It's not a choice. You're forced to pay for the pension system in Denmark and most other countries if you're employed. The only thing governments have to do is to use that money for actual pension funds instead of embezzling it, and to calculate the contributions on a reasonable basis with reasonable extrapolations about inflation, i.e., to properly finance these funds now and not abuse them for other purposes.
It's mysterious why they haven't done that despite the fact that the demographic problems were known to occur up to 40 years ago. But you see the same thing with housing prices and rents, forthcoming problems were already obvious 20 years ago in every country, yet only few have tried to deal with them in time. Maybe someone else can explain where this inertia comes from, I always found it strange.