Could you remind me the last time FDIC has been unable to pay?
If enough people go to the same coffee shop all at the same time, there'd be carnage. Fortunately, shit like that hasn't happened yet, so while it remains a metaphysical possibility, color me not worried.
It is Bank deposit insurance. It is not banking system insurance. It was designed to prevent runs on individual banks, not on the entire banking system. It was dangerously undercapitalized in 2008 and required a bail-in and also had to hike rates to repay the emergency loan.