Nope. They make the money for the rewards by charging merchants higher fees if you use a rewards card vs a non-rewards card.
My standard merchant fee rate might be 2.4%, but if you use a 'airline miles reward card' with me, I may end up having to pay 2.9% or 3.4% (or more). I can't not take your card - against Visa/MC terms of service - so I'm stuck paying for your 'rewards'.
My standard merchant fee rate might be 2.4%, but if you use a 'airline miles reward card' with me, I may end up having to pay 2.9% or 3.4% (or more). I can't not take your card - against Visa/MC terms of service - so I'm stuck paying for your 'rewards'.