If the power goes out, I can't get any cash. I don't keep any meaningful amount cash on hand and neither does anyone I know, including my elderly relatives. Most of the stores I shop at won't actually be able to sell me anything, because none of the products have price tags and I sincerely doubt that any of their staff are trained to revert to pen-and-paper accounting. Even if they did manage to keep things running, they'd likely run out of change by the end of the day. The grocery stores are JIT and have no more than a few days of stock of anything; again, I doubt there's a manual backup to their reordering system.
Maybe things are different in countries with less reliable infrastructure, but I just can't think of a scenario in which cash would gain you any appreciable amount of resilience without much wider systemic changes. So much other stuff beyond payments is wholly reliant on technology. I'm not sure that would be a wise investment versus improving the resilience of power distribution and network infrastructure.