This is actually exactly the case that I had in one trip to Andorra: the power was down for 2 hours while we were choosing equipament for skiing. The shop had no issues getting our orders done though, because they just manually filled the orders with pen-and-paper and did the payment with a credit card terminal connected to a smartphone.
If your city has an extended power outage, the cell nets could easily be down as well.
And I am not saying that you shouldn't accept money as backup, of course you should. But what I am saying is that you can still accept credit cards even during most power outages.
Same as Software Engineer, it is impossible to have perfect, 100% reliability, but it doesn't mean we can't improve from 99% to 99.9%, for example, to have a better service.
Without electricity the water system depressurized, which contaminates it. After about a week the sewage pumping stations have backed up so the sewer system is starting to fail.
Modern cities cannot operate without electrical power given their scale and density.
It is bizarre to think the biggest problem is "how do we keep a transaction of value?"
Like, just declare an emergency and let business owners be reimbursed by the government.
Credit cards and payment networks have always explicitly supported "Offline" processing like that.
The kind of fraud that system enables isn't really common.