Not to be completely off-topic, but that's not the full story. Merchant and transaction fees are what turn the engine, not just interest. AMEX, for example, made their start entirely on transaction fees as they didn't allow balances on their charge cards. Clearly, the interest game is a major benefit, but merchant fees are still the bread and butter and outearn the interest for several banks.
There is a reason the super-premium cards offer huge signup bonuses, give mega points, and have insane APRs of 25%+. Yet they only go to high credit scores with good credit history and good incomes. People who generally won't ever carry a balance. Why? They charge more for those particular transaction fees.
To dumb it way down. An order costs $10 at the grocery store. Someone pays cash for the order- store makes $10, right? Now, I go and buy that same $10 order with a super-premium card that charges the grocery store 2.1% + .10 on the transaction. That $10 order now has a merchant fee of $0.31- meaning the grocery store only makes $9.69 on that transaction. Does the supermarket just take the hit on that and lose 31 cents profit? No- they raise the price to $10.31. Now I pay $10.31 and get 3% back (which, coincidently in this case is 31 cents)- making my net purchase still $10. Meanwhile, cash person spends $10.31.
Hence, they subsidized my points and the big bank earns more.