[1] I have a card that gives me 5% cashback in gas, groceries, and books up to a limit that does not often surpass what I spend and some rotating 5% cash back cards, in addition to a 2% general spend. I do not pay any annual fees for using the cards.
If you only use the card to spend $100/week on Groceries, you get $312 in cashback rewards. Subtract the $75/yr fee, and Amex paid you $237 to use their card that year.
(Amex isn't the only card like this -- there's lots from MasterCard and Visa as well. This card in particular just happens to be one of the rewards cards that I know the details of.)
But unrewarded cards aren't really any different. Most merchants still have to pay the same high fee for them. Since the bank/processor is going to take the maximum amount of money they can regardless, and most merchants will have to pay that full fee regardless, you might as well use a rewards card over an unrewarded one.
American Express cards offer the best rewards, but the cost to the merchant is much greater. Many shops or restaurants don't accept AmEx, and sometimes those that do will say they prefer you to use an alternative card.
But within one network, I think it's correct that the cost is the same regardless of the card's promotion.
Depending on agreement, card type, and other factors, the swipe fee is sometimes higher than 2%, so I don't always get all the difference back.