Is that what you think large businesses do for treasury management? Just keep opening bank accounts until they've got one with every bank in the US?
If FDIC wants it to be possible to insure that much, they should cut out the middlemen and financial engineering requirements and just insure deposits of every business to that amount. If they don’t want to insure that much, then IntraFi and other similar services should be illegal.
Why though? The "$250k per bank" rule is clearly a feature of the system, not a bug. If the FDIC wanted to have the insurance limit be across all banks, that's how they would've structured the rule.
But they didn't, because their purpose wasn't to provide unlimited protections to corporations from bank failure, it was to limit the impact of any individual bank's failures and decrease the likelihood of bank runs.
The current rule does this effectively, and encourages larger businesses to diversify their assets while also providing significant downside protection to many individuals and small businesses.
FDIC doesn’t want to insure that much against a single bank failure. Encouraging diversification of large balances helps the FDIC’s goals, since it reduces the impact of single bank failures and reduces the possibility of single failures turning into broader economic collapses without increasing the cost to the Treasury of a single bank failure, which is an efficient way of promoting the purpose for which the FDIC exists.
It might be efficient for the FDIC to require complex and expensive financial engineering just to keep operating capital safe, but it's hostile to businesses, especially small ones, and is out of reach for many.
The FDIC exists to protect against a general collapse of banking like the one that preceded the Great Depression, not as a generalized subsidy to business.
If you'd like to argue that the FDIC should go further so as not to subsidize people with shit-tons of cash, I'm certainly open to that. But the increased regulatory complexity might not be worth the total risk reduction, so I'd want to see some math. I suspect it's mainly a red herring, though, as I couldn't find any sign that Intrafi is a particularly large business.