The only factor that suppresses that fundamental reality is consumer confidence. Deposit insurance, an institution designed to shore up a bankrupt system, contributes to the sense of confidence. Even small depositors' actions, like withdrawing a bit more cash, undermine that confidence. Despite the appearance of stability and soundness, then, the foundations of modern banking are actually extremely precarious. It would only take the right kind of crisis, or perceived crisis, to throw the entire system into chaos.
Bank runs and the threat of bank runs serve a heroic function in a free society.
They spur banks on to be more careful in the conduct of their business. We need more, not fewer, of them.