FDIC eliminates most of the risk associated with lending money you don't have (
Fractional-Reserve Banking). With FDIC, banks can lend, and earn interest on, money they don't have on deposit.
Banks have a deposit requirement, usually about 10%. If they have $1,000,000 in depositors, they can lend $900,000. So the've lent $900,000 but still owe, on demand, $1,000,000 to the people who entrusted their money to the bank.
It's inflationary, - they just created $900,000, for which they are earning 7% interest.
There are many folks, myself included, who think that the benefits of money creation should accrue to the public, rather than private interests like the Federal Reserve System.
In general, shifting to such a system would involve outlawing fractional reserve banking, and using Government-Issued Currency, rather than the (Private) Federal Reserve Notes. This would generally mean and end to receiving interest on demand deposits - to earn interest it would have to be an investment, like a money market or a bond fund. It would also mean and end of the federal government issuing debt. It would mean an additional $300B of revenue for the federal government each year. Because all of the bank-created money would have to be replaced with an issue of $7T in new currency, the federal Debt would be eliminated, leaving anotehr $280B a year, not spent on debt service, for the Federal government to spend.