Your acting as if the FDIC only exists to cover a massive systemic failure. In the event of something like that additional intervention may be need sure.
However, the FDIC covers all banks, and is generally involved with smaller banks fail and they are they to insure whatever balance the bank could not cover with its remaining assets when it failed.
I’m not actually aware though what the last incident they actually had to pay out was though. Looking through their historical data on bank failures every one I’ve seen says the insured accounts were assumed by another bank purchasing up the failing bank.
One of the largest recent FDIC payouts was IndyMac. I'm not sure if this was the most recent one, but certainly one of the most recent big ones. They were so bad that no one wanted to take them over! And the other banks were in such a bad way at the time, the FDIC couldn't force through a shotgun wedding with a semi-willing suitor. So the FDIC got stuck with them.
But worse, thousands of the individual depositors and businesses who banked at IndyMac were over the FDIC limits and they lost, collectively, hundreds of millions of dollars. The FDIC insurance limit at that time was $100k per separately-named account per bank; it is now $250k. And the $250k raise was, in a surprisingly kind move, purposely made retroactive to help cover some of the losses that people had suffered during the GFC under the previous lower limit.
And still, despite all that, lots of people lost lots of money when the bank went under:
However, the FDIC covers all banks, and is generally involved with smaller banks fail and they are they to insure whatever balance the bank could not cover with its remaining assets when it failed.
I’m not actually aware though what the last incident they actually had to pay out was though. Looking through their historical data on bank failures every one I’ve seen says the insured accounts were assumed by another bank purchasing up the failing bank.