Fearing the asset-quality signal revealed by such a run at one bank, depositors could start running on other banks too, especially ones with similar assets and a full-fledged banking panic takes hold.
When this happens, the entire banking system is at the risk of being disintermediated; payments and settlements of financial transactions can come to a standstill; banks have no capacity on balance-sheet to make new loans to new entrepreneurs, first-time home buyers and old families; the economic activity can come to a grinding halt.