$100 under your mattress for the future is not worth nearly as much as giving that money to a friend to help them cover rent today
You're not going to lose access to your bank account because the bank failed; the FDIC handles that. It just moves to a different bank over the weekend.
Locked out because Chexsystems thinks you're a financial criminal is more in the direction of possible.
Has happened to more than one bank I've used, in more than one country.
I've also had a bank freeze my account temporarily (for over a week) because some risk algorithm somewhere thought fraud was occurring.
All those times, having a bunch of cash handy was very useful.
As for hard assets: they make a decent hedge against financial shithousery.
In a natural disaster type situation it could easily be the difference between being able to get what you need stay put the whole time or running out of some supply you didn't think you'd need and having to evacuate half way through the follow-on mess and losing quite a bit to looters and/or the environment.
The other person who replied mentioned more mundane stuff.