No they don't, they would prefer you carry a balance so they can charge you interest every month in addition to the 3-5% they charge the merchants for everything you buy.
LOL, One of my relatives who paid CC interest for years tried to tell me that years ago, recently he had to give up his credit cards for debt consolidation.
Perfect example : Back when I traveled frequently I once misplaced a bill and Chase charged me both interest and a late fee (owch!)
I immediately paid the entire balance with bill pay and then called them a few days later and politely and calmly asked them to refund BOTH to my account (remove both charges from my balance) .
Chase reply “No problem.Is there anything ELSE we can help you with?”
I answered : “No, but I love my chase”
They call people like me who pay off every month "freeloaders".