Earlier quoted context omitted.
The banking system was already very sophisticated pre-1930s.
My question was, specifically: It's 1903, you deposit your life savings into your local bank, and a week alter it gets robbed. Do you get any of that money back? Or are you now broke?
In most cases, even a large robbery wouldn't ruin a bank: They could borrow against or sell their mortgages to another bank for cash to pay depositors.
This is different than a safety deposit box: The fine print is that you are responsible for its contents and if the bank is robbed, they will not replace the contents or reimburse you.
So, if you put your life savings into gold and put the gold in a safety deposit box, you lose. If you put your life savings in a deposit account, you will be reimbursed unless the bank fails outright.
(Prior to the creation of the FDIC in the US or deposit insurance in Canada).