No, that's actually a pretty reasonable idea. Given that they've never lost a cent of money, can take more from the other banks if they need to, and are ultimately backed by the people who print the money.
You don't understand insurance or how the FDIC works.
Not even remotely true. In the 2008 financial crisis, between 2008 and 2012 , there were nearly 500 bank failures, and more than a trillion in assets involved and the FDIC covered every cent labeled to be covered.