We had a long power cut that went on for many days. The supermarkets shut at first because, why not. As things went on they had customers to serve so they had to sell, I remember that tesco set up a table at the store entrance with the shop manager and a few assistants. You told them what you wanted, the assistants got it. They took cash only [0]. It worked.
Tangential to the article, what would happen today? People are carrying much(?) less cash, card only point of sales terminals are blooming, I just 2 days ago went to top up a spare mobile phone and the vodaphone store told me they'd no longer take cash.
Notes & coins don't need electricity to be acceptable. We may be creating a very fragile alternative because things like comms and power look increasingly reliable so why lean on them ever harder, but they will go down someday, that I guarantee, and the harder we lean on these things, they harder they will drop us when they vanish.
And we may have short power cuts due to human nature but there are things like solar storms. We know they are coming but aren't prepared for them. So what then?
[0] which they must have got from somewhere. I don't remember how the banks were operating.
I don't know if this is still a thing, as cards are no longer coming with the raised characters required to take an imprint. But perhaps the imprint is no longer necessary, and simply writing the information suffices.
There are (obviously) more avenues for fraud without online verification, but the techniques of fraudsters are no longer optimized for running physical cards either.
The more significant thing that we've lost is a cashier/manager being able to exercise some level of intelligent oversight to judge whether a transaction is likely to be fraudulent. But then again, perhaps a store being cleaned out of its entire inventory of eg Tide because of a long term power outage isn't that big of a deal either.
Until the Piggly Wiggly supermarket introduced the self-serve concept in 1916, you would go up to a counter and tell a clerk what food items you wanted, and they would get them for you. So your analogy really is the 1920's version of the self-checkout!