> I'm aware of merchant transaction fees, but they're insufficient as an explanation. Just run the numbers.

I don't have to run the numbers, because I read the article where they did the actual research with real numbers, not your back of the envelope estimating, and they came to the opposite conclusion:

| This leads to our second hypothesis: High interest rates are necessary to recoup the high cost of rewards. However, our analysis shows this is not the case. Rewards expenses are more than fully covered by banks’ interchange income—fees collected from merchants based on purchase volume. On average, interchange income amounts to 1.82 percent of purchase volume, while rewards expenses are 1.57 percent.