If a run begins on one particular bank. couldn't the govt, instead of chloroforming the whole institution (another quote from George Bailey), merely shut it down temporarily and impose temporary restrictions on the amount of money any given depositor could withdraw, along perhaps with requiring the bank to liquidate some of its assets to bolster its cash on hand?
That sounds far more likely to cause widespread panic than making depositors whole the next day or so. It seems to me that depositors made whole would mostly deposit the money in some other bank, as a message is sent that depositors are safe, whereas if access to your money is restricted, that means that depositors WILL be affected (limited access to their own money) which creates an incentive to keep money as cash under the mattress, crypto, etc. These are not just theoretical considerations - Argentina once went down the restricted access route (granted, this being Argentina it applied to all banks, not just some) and it was catastrophic, not least because it restricted people's ability to spend. But if applied to just one or a few banks, I don't see how it would save them - depositors would surely withdraw, spend or transfer every penny they could, as fast as they could, out of the restricted accounts, have any income deposited into another bank, etc.