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.
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.