Cards don't make money from their fees. They make money from people who fail to pay and then pay the ridiculous interest.
Do people who pay ridiculous interest qualify for 2% cards? Honest question; I don't carry a balance so have no idea what is advertised at other types of consumers.
Interchange fees seem to be a sizable portion of revenue. Discover has listed them as 29% of revenue, BoA at ~$10B annually…