I don’t follow the math. A bank failure is a bank failure. There’s no difference to the FDIC between 100 depositors with $250k swept across 100 banks and 1 depositor with $25m.
If the deposit is 250k across 100 banks, and only 1 bank fails, FDIC is only on the hook for at most the 250k.
Now multiply that by number of depositors. It's RAID for banks. You're gaining fault tolerance by decreasing the impact of any particular failure.
Just wanted to say this is such a great analogy. Thanks.