In USA, I don't think there is any problem, just cash unbalance between small and large banks.
In digital era, money withdrew from small Bank A will end up in large Bank B, Bank A just need to borrow them back from Bank B to deal with cash shortage. And that is why JPM and other large banks who received those money are willing to help the small banks. Money does not go anywhere outside of the banking system. However, this is a good chance for large banks to wipe out competitors by refusing providing help
Credit Suisse's case is little bit more complicated, since they use Swiss Franc, could not get that help from other Swiss banks if the withdraw is in form of USD, they have to borrow money from withdraw destination bank, and when that is not feasible, they were wiped out