These issues are all going to be at business banks (and even larger banks that do both business and normal are often actually separate entities).

I know people who had their checking and savings at Washington Mutual when it failed in 2008.

The FDIC arranged for Chase to take it over. Nobody lost any money, and nobody I know had any problems with checks clearing or withdrawing cash at ATMs or paying their rent or mortgages.

I think the demise of Washington Mutual is still considered the biggest bank failure in US history, it happened while quite a lot of other bad things were happening, yet depositors ended up being totally fine. The systems in place for this are actually really good, and the FDIC is fast and competent.

FDIC takes almost no time. From their website (https://www.fdic.gov/consumers/consumer/news/cnfall14/miscon...):

The FDIC almost always pays insured depositors within a few business days of a closing, usually the next business day. Payment is made either by providing each depositor a new account at another insured institution or by issuing a check to each depositor.

What kind of nonsense is this. if you are under the $250k there is no disruption at all. The average person's money is perfectly safe and protected.

FDIC says SVB customers will have access to insured funds on Monday, so seems like the answer to your question of how long it takes is “next business day”.

No rational reason, however during bank runs rationality tends to go out the window and even banks that are perfectly safe on paper can find themselves in trouble.