The FDIC is the insurer of last resort. They don't get to go bankrupt. They also wield the authority of the federal government, which is the authority of the p

The FDIC is the insurer of last resort. They don't get to go bankrupt. They also wield the authority of the federal government, which is the authority of the people, represented more or less collectively, and which is operating under the principle of maximizing social utility, in contrast to the insurance company in your metaphor which is trying to maximize profits for its shareholders.