FDIC is not going to help you in a bank run. It does not work the way most think. IDEAL is different from REAL.
Keep some cash in high quality fire proof safes at two separate storage facility companies with 24 hour access near your home....enough cash to hang for at least 30 days.
does it really matter? its more common that people have a shitload of debt. so if everything collapses to nothing, then we can just set the banks on fire and have no obligations. i think a better plan is to grow some vegetables in the back yard and keep the pool filled with water.
It's not reason to panic, but it is still better to have cash on hand, rather than have $100k tied up in an insolvent bank, waiting months or even more for the government to sort out the insurance payments. A prudent individual would have their cash spread across several different bank accounts, with some held abroad, and say 3-6 months living expenses in cash at safe deposit boxes and at home.