> you save now so you get money later.
How do you save labor for later? Current retirees need young folks to do the work they cannot do, and thus those young folks are paying in today.
When those young folks retire they will be relying on even younger folks to do the work for them. If there are not enough younger folks to do that work, the money saved between generations will become relatively worthless.
Thought another way: The same amount of labor needs doing. If the current generation of workers stops paying in (read: working), then the entire system stops. One generation saving more (or being larger) than the next doesn't change much other than that saved wealth chases a decreasing amount of available labor once that generation retires. Quality of living will be predicated on the amount of available labor - not saved capital.
It gets a little more wishy washy when you can plow capital into long-lasting infrastructure, international wage arbitrage, etc. but in the end you simply cannot run retirement systems if you have less labor available while keeping the same quality of life for all parties. Someone is going to lose.