There's a lot of truth to that (cash paying customers pay the same, even though the cost to serve them is less).
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.
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.