You don't want to get all sweaty when the news starts coming in about the final death throes. Even if there's a guarantee (and there are in many countries), I would imagine there would be a period of limbo where it's very hard to get a hold of people who can assure you.
Meanwhile, there's plenty of other banks who seem a lot less likely to fail.
I also could tell a story about people losing access to their money for weeks, waiting on the FDIC, when IndyMac failed at the start of the recession. But it is not my story to tell as it did not affect me, and it was also one of the largest bank failures in US history, at a time when the FDIC was already undergoing stress, so I doubt it was malice.
I just wouldn't count on FDIC insurance to save you in the short-term if shit starts to hit the fan. Have a cash reserve.
Edit: Here's an interesting graph to ponder https://fred.stlouisfed.org/series/BKFTTLA641N
The first major cluster of failures actually preceded a crisis(the S&L crisis) and fell off rapidly after, whereas in 2008 the cluster was timed with the recession and had a longer tail of failures afterwards that continues to this day.