The belief was that failing to cover those uninsured deposits ran the risk that bank runs could spread to more banks. Covering those uninsured deposits was intended to calm depositors in other banks, which would thereby make more bank runs less likely.

Since then, some people have called for officials to cover all deposits in the banking system, insured and uninsured, in order to keep people calm and prevent more bank runs. In other words, they are suggesting that the $250,000 deposit-insurance limit be lifted entirely. 

Yesterday, however, Treasury Secretary Janet Yellen told the Senate Appropriations Committee that she is not considering "blanket insurance" to U.S. banking deposits. She said that officials would cover uninsured deposits only when a failing bank constituted a "systemic risk" to the entire banking system.

Nonetheless, it is difficult to imagine that U.S. officials will leave uninsured depositors hanging in future bank failures, given that they just covered uninsured deposits at Silicon Valley Bank and Signature Bank. In future bank failures, uninsured depositors are going to be clamoring for coverage too, and they will be citing Silicon Valley Bank and Signature Bank as precedents. 

The dark irony here is that by covering uninsured deposits at Silicon Valley Bank and Signature Bank, officials might actually be encouraging bank runs on an industry-wide basis in the future. That's because everyone knows that the federal government does not have anywhere near the money to cover all the money on deposit in U.S. banks.