I have been following along with this New York Times series on the costs and rewards of using debit and credit.
The latest installment has been whether it is ethical to use credit cards with rewards programs when those rewards are subsidized by other consumers, generally less well off, who don't use credit or can't use credit (because they are not eligible). You can figure out how much your card cost by going to true cost of credit.
We don't use credit cards, but we do use our debit cards with signature (which is more expensive for the retailer) for just about all our day to day purchases.
Retailers, over the years, have figured out that people who use plastic spend more money and buy more stuff, so more and more retailers accept credit cards. It also costs a pretty penny for retailers to process cash, i.e. theft, counting, banking, etc. so the idea that cash costs less for retailers may not be true.
But I think the question that the NYT poses, should poorer consumers subsidize richer consumers rewards is a very interesting one. Problem could be solved if more retailers offered a cash discount to those who use cash.