FRB succeeds because these institutions accept each other's IOUs, withdrawal panics can be stopped with banking holidays, big banks will bail in each other to advert a crisis and then bail outs from the government who consider these banks too big to fail.
MtGox wasn't a bank but imagine if there were other MtGoxes and they were chummy with each other? They would had rescued MtGox and there may had been no Bitcoin bust in 2014.