I would say 'yes'. Banks should start offering fully insured accounts (maybe they already do) and those accounts should cost more and possibly have different liquidity profiles.

Fully insured by whom?

A re-insurance company probably, or the FDIC which would charge a premium for the excess insurance.

Why banks specifically? Should there be insurance for AWS and Github accounts?

> maybe they already do

"Insured cash sweep" (which is basically "RAID for banking")

There already is DR and business continuity insurance so non-financial assets have an entire industry around insuring against events there.

Cash sweep is insured but only to a limit, there's nothing magical there and the underlying securities have default risk (or breaking the buck).

at this point, who could doubt that AWS itself is faaar too big to fail?

North of $250,000 it's a bet. If you're Roku and you have hundreds of millions of dollars in a single bank, that's absolutely a bet. Companies can get private insurance to cover money in excess of the FDIC, but they didn't. And now no one will, because billionaires know they can threaten bank runs and violence to get bailed out.