Sure, but cash back is a kind of marketing trick which makes the card user more willing to spend and use their card. It's this little extra which pushes you over to buy something because, hey, I get my cash back.
There is no free lunch. Someone has to pay the cash back and we like to think it is the merchant, but in the end it is the consumer who pays for all these cash backs and card fees.
Well, specifically, it is the other consumers who frequent that merchant and pay in cash/debit. In the US anyway, at any business that does not charge CC fees, people who do not pay with a CC are subsidizing people who do.
Businesses generally are happy to pay the CC fees, because in the local minimum in which we exist, that is the price to pay to access a large segment of the population's purchasing power. Businesses are not required to accept CCs, and some do not, but those that do do so because the income brought in by the people with CCs who would not show up to a cash-only location outweighs the price of the CC fee.