Credit cards and cash have their place but the story being told doesn't track with experience.

First, businesses are increasingly differentiating pricing between cash and credit card - this is most obvious in gas stations where the price you see on the big sign is the cash price and not what you practically end up paying. Or the various restaurants and other businesses that offer cash discounts. While this is relatively new, the earlier manifestation of this is the credit card fee - eg try paying your tuition or utilities using a CC and you'll immediately find this option costs more.

Interestingly all the above usually hover around 3% so it's tellingly the rate the merchants themselves perceived CC use and infrastructure cost them.

Second, credit cards are clearly good for business volume. Most people have had the experience of wanting to buy something unplanned and not having the cash on them, but buying it anyway via credit card. On a larger scale, hard to imagine on-line shopping without a credit card.

Third, I don't find cash-only businesses cheaper. In my town there's a cash-only barber, pizza place, and ice cream shop and they cost just as much as the credit card taking ones. In every case the dynamic is there are long running businesses with sufficient clientele that they never bothered, but they don't use absence off CC fees/infrastructure to generate a consumer savings.

Fourth, poor people can play the point game too. As a broke college student I was very fond of my Exxon Mobil card that gave me cheaper gas. Now I don't really care about an extra ten cents on a gallon as much.