Companies like Stripe shield you from the intricacies of interchange pricing but if you operate on interchange + (meaning, the merchant account provider is charging you interchange + X %), you see that processing corporate rewards cards are the biggest killers, because you are essentially covering their 2% cashback programs. Additionally, some of that cost is insurance. If you have a fraudulent charge on your card processors work with your banks to cover some of that money, which they make from the overall % of total volume.
Not saying any of that is right, or an ideal situation, that's just the why.