It pays significant disability and survives benefits which has little to do with investing and everything to do with insurance. So consider SS as insurance in case of a long life.
Some people will live well over 100 so finding the "correct" amount of money to save is overkill for most people who die far younger than that. If you invested a portion of your savings each year and pooled you money with 10,000 other people your age then paid dividends from that to the survivors you could save less money and still not worry about running out. Granted if to many people lived until retirement age you might need to reduce benefits. Granted you would not be able to give people money at the time of your death but if your single what's the point?
Now the implementation of social security is broken in several ways but minor changes in retirement age will fix the "benefit gap" long before it runs out of money. The basic problem is people are living longer so they need to increase average retirement age. The surplus was also invested in government bonds with terrible long term returns etc, but when you consider how much more important the first 20k/year is over the next you might consider guaranteed benefits even at high cost are worth a lot more than the simple math would suggest.
PS: There are a lot of things I hate about SS, but it's not really a Ponzi scheme.