If the banks are capable to pay out all the deposits to the people, who want to withdraw them, there's nothing to worry about.
The real problem will appear, when the banks don't have any money to pay their depositors. It seems that First Republic Bank is handling the situation very well. It's normal for the banks to start facing difficulties. The interest rate hikes are intended to drive the financial sector into stagnation. This will lower the inflation and the economy will stop depending on the money printing machine(at least for a while).
The key word here is "if". The very architecture of the modern banking system is such that not a single bank in the world can withstand the "raid of depositors." Typically, banks' reserve requirements for equity capital do not exceed 10-15% (and this is an optimistic estimate). No one knows how many paper unrealized losses that arose after a sharp rise in the key rate are in reality on the balance sheets. The real problem will appear, when the banks don't have any money to pay their depositors. It seems that First Republic Bank is handling the situation very well. It's normal for the banks to start facing difficulties. The interest rate hikes are intended to drive the financial sector into stagnation. This will lower the inflation and the economy will stop depending on the money printing machine(at least for a while).
