That got me wondering why anyone leaves amounts over 250k anywhere else.
If you have 5m are you going to open 20 bank accounts? If there's a wobble you'll need to dig out a lot of credentials to move your money, and you'd end up moving it to a TBTF anyway.
If you have that kind of money in cash you pay someone to do that for you. If you want access to your money you don't juggle credentials, you call your banker and ask.
Actually even if you don't have millions you can use sweep accounts that automatically spread money across multiple bank accounts. Fidelity has one that anyone can use.
If you have 5m are you going to open 20 bank accounts? If there's a wobble you'll need to dig out a lot of credentials to move your money, and you'd end up moving it to a TBTF anyway.