I'd recommend reading up on the Federal Reserve (The Creature from Jekyll Island), the modern financial system (any of Michael Lewis's books, especially Boomerang and The Big Short), and maybe the first global banking families (The Medicis: Power, Money, and Ambition in the Italian Renaissance). We're talking about the power structure of the world here and it's good to be informed on the main points.
I still suspect that the securities mentioned are your own securities rather than the bank's, which makes it totally sensible that they're not covered by the insurance.
"Own nothing, but control everything." -John D. Rockefeller
edit: good note from /u/snowwrestler below:
> > It's not the cash/securities that Robinhood holds as part of their business, it's the one they hold for you. You may well choose to hold 100% cash or 100% securities.
> If I'm holding 100% securities, a) SIPC offers me no protection from losses, b) I better be making more than 3% return, and c) I would not call that situation "a checking account."
"I bought 100 shares of Acmecorp, then Robinhood shuttered their doors and said they sold the shares to fund their yacht."
The SIPC's job there is to reimburse you for 100 shares of Acmecorp as of now; they're not going to let investors cherry-pick and say "but they mishandled the account during the one day it was at its peak and I want that price!"
I don't understand what a "checking account" is that guarantees 3% interest and is covered by SIPC instead of FDIC.
Because if it is, then this is basically the same. Your cash is fully insured, but obviously your investments run investment risk.
If Robinhood automatically converts your money into securities, then it's a different matter. It sounds unlikely to me that any bank account would work that way, but I don't know how Robinhood works.