I think you meant to say here and unlike banks, because banks absolutely do not need to have sufficient funds to cover all customer's savings.
Unless.. are things different in the US? It's been a decade since I've read the Bank Act (Canadian), and when I did, only 5% of customer's account holdings were required to be held in tangible assets (gold, cash, etc), and inspected yearly by the Minister of Finance.
And I believe even that requirement has been dropped.