I disagree with the applicability of your fundamental premise about risk. It seems reasonable when talking about setups to backstop risk or otherwise move it around, but the amount of risk can still be increased/decreased by adjusting the fundamentals. The straightforward way to reduce the risk of running out of slack in the system is to have more of a buffer to begin with, which is why I mentioned reserve requirements.

Furthermore I'd argue that insuring deposit banks through the asset-limited FDIC is yet another setup to socialize catastrophic losses. If bank deposits were guaranteed by the Fed directly, the Fed could print an unlimited number of dollars to make depositors whole, thus completely eliminating the risk that a USD-denominated deposit simply vanished. (The realized damage would instead be expressed as monetary inflation)