And if the FDIC didn't have enough money, the government would start printing it like crazy and the US would start looking more like Venezuela in a very short period of time.
Bank collapses happen during times of deflation. In that environment, printing money like crazy just returns the financial system to normal, low levels of inflation.
Small amounts of inflation are a good thing. Deflation in a currency is almost always bad, and this is why limited-issue crypo like bitcoin will never replace real currencies.