Think about this with some numbers: if there are 100 banks, and every business puts 1% of their cash into each bank, the overall risk is the same as if 1% of businesses put 100% of their cash into a random bank out of the 100.
The cost to FDIC if an individual bank fails is the same in both the above scenarios, even though in the first businesses put a lot more effort into spreading out their funds. It looks less like it could have less risk to the FDIC, but really isn’t making any difference.
The odds that 100% of businesses each decide to pull their money out of the same bank at the same time is less than 1% of businesses who invested at the same bank pulling out their money. Especially if they are in the same industry and know the same people urging a sudden withdrawal. Maybe even mostly located in the same geographic region.
But if the FDIC insures all deposits anyway, then there would never be a bank run to begin with because nobody would panic that they wouldn't get their money out, so spreading risk among multiple banks is a "solution" to an artificial problem.
It's a solution to a bank run because of fear of the banks going under. It's not a solution to a bank run because an industry needs cash quickly. For instance, Silvergate had a lot of crypto firms as clients, and in late 2022/early 2023 all those clients needed cash. You can imagine something similar happening in other industries.
I don't see a problem with a rule or regulation that limits individual daily withdrawal limits. That would solve that specific issue as well, and anybody who needs to withdraw more than that per day clearly has enough funds to have accountants that can coordinate across multiple banks.
The cost to FDIC if an individual bank fails is the same in both the above scenarios, even though in the first businesses put a lot more effort into spreading out their funds. It looks less like it could have less risk to the FDIC, but really isn’t making any difference.