If a retailer can't process transactions (e.g. look up prices) being able to give them a piece of paper isn't necessarily better than trying to process a credit card.
ADDED: And yes. Sometimes places are simply not setup to be able to take cash.
The point they’re making is that if there is a system failure which makes card payment unavailable, the failure could also have taken out the cash register entirely. And because most products only have a bar code on them which has to be scanned to get the price, it’s possible that the store can’t sell anything (unless they want to look up the price of every item at the shelf).
The interesting thing is that it was only the last mile of the payment processing that has failed whereas the core payment processing (payment networks) and intermediate layers (acquirers and mobile wallet infrastructure) have held up.
Reports about failing Apple/Google Pay actually pertained to the POS terminals the payment terminals are connected to, and not the payment infrastructure itself.
Another interesting takeaway is that we used to have an extra layer of redundancy available at the last mile of the payment processing: slip machines. They were a workaround and a fallback for exactly this kind of problem where the payment could not be processed electronically, a card payment slip would be taken, and the payment would be later processed manually.
However, with the uptake and the scale of electronic payments, card payment slips are no longer a thing mostly due to fraud related issues, plus the inconvenience of having to keep such a large contraption under the till. Even where still available, it may no longer be possible to use it as more and more debit (in particular) and even credit cards do not emboss the card details on the plastic/metal anymore.
To this point, I have shopped in grocery stores during power outages. The checkout terminals usually have battery backup and a local copy of the current prices to enable processing cash transactions.
ADDED: And yes. Sometimes places are simply not setup to be able to take cash.