If Social Security did not exist, many elderly individuals likely would have saved somewhat more and worked somewhat longer,

Old people working longer to pay for retirement fucks over younger people trying to move up below them. And save for their own retirements

If one generation works longer to save for retirement this stagnates the job market for the generation underneath them. And makes it so they have to wait longer start saving for their own retirement which in turn keeps happening to every generation below them. Having to wait and work longer then the generation before them.

Social security helps alleviate that problem by guarenteeing a fixed source of income to the older group so the younger group can move up faster and have lucrative enough jobs to save and spend money in the economy.

and many might live with their adult children rather than in their own households.

That's Never really been a US cultural thing for the past 70 ish years.