My understanding is that yes, you're not covered if the bank suffers losses and passes them on to you. The entire industry is one giant moral hazard due to complete lack of skin in the game on the part of the banks. They don't own the money and aren't responsible for catastrophic losses (see the '08 and previous bailouts), but they control it and keep the upside. You're right, that insurance sounds like garbage, but I haven't bothered to dig into the details. Caveat emptor!
"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."