It isn't just about out performing. An insurance policy is supposed to be with an asset that would be expected to do well if the underlying asset that is being insured were to collapse.
FDIC is insuring bank deposits which are being invested into bonds by the banks as well as mortgages. Therefore what asset would be expected to go up in the event that bonds and mortgages were to collapse? Bonds go down when inflation goes up, mortgages collapse when you have a recession. So then what asset goes up when we have high inflation (commodities). What asset goes up when people lose jobs? (Obviously you can't be invested in stocks, and you need something that is international)
Therefore it seems to me that Gold, Silver, or some other commodity would make sense. You want something you can hold for decades without losing its value. Easy to own and easy to store.
Obviously you need a safe place to store gold, what better place than a bank?
Chase bank has 4,700 branches, so even if they hold a small amount at each bank branch that is insured by FDIC you could easily disperse the risk.
There are 72,000 bank branches in the US and of course we have Fort Knox. The FDIC could have been buying gold year after year with the premiums.