Agreed. We've paid off everything every month for well over a decade, pushing two. They love us. The reason is -- they get money from the merchants just for us using the cards. (The original business model of the cards, long before exorbitant interest rates and penalties.)
They especially love us when we run large items through a card and pay them off.
Considering most good cash back or points cards give roughly 3% of the value of the purchase back to the card holder, that would indicate to me that the merchant is paying at *least* 5% and the card company is keeping 2% or so.
The very nature of the transaction being against small business, whenever we do business with a small business or friends, we pay them in cash. No point in them eating 5%+ of the sale so I can have 3% of it as a cash-back award, and the card company can have 2%. But large businesses that make it easier to pay them with a card than pay them cash? They can eat it... even though we know they simply pass it back to us as a higher price tag.