I think the original concept when Touch Tone shopping was first proposed was that the customers would be pre-registered with an existing account. In those days, credit was only approved in advance or the goods were COD. I don't think there was as much intentional fraud against the corner grocer or pizza delivery place. There were some accident screwups where a customer ordered the wrong stuff and refused delivery or forgot to pick up a pizza.
In today's Internet world, the big theme is instant gratification and anonymity. That allows for more opportunities for fraud. No delayed credit review first.
Further, unlike the world of 1964, we are more anonymous from each other and our merchants. Supermarkets are much bigger than they were back then and the old corner grocers no longer exist. Today's convenience stores are very anonymous.
The old corner stores had to eat a lot of bad credit from customers and their prices were higher. Supermarkets, by offering no delivery or credit, could offer lower prices. (Initially trading stamps were offered but then discontinued to save money and lower prices).
Ironically, today supermarkets do take credit cards which annoys me since it adds to the cost of the food. Indeed, pizza places, fast food, and convenience stores take credit cards too.