Once in a while. However the truth is the large people who collect the 1% and pay off their card every month are the people who don't. These people are customers year after year, and often spend more on their cards (they tend to be higher income), and the bank gets their 2-3% from them (2-3% after rewards)

People who don't pay their card off also are on the look out for lower interest rate cards and switch all the time. they in reality are not paying the very high rates on cards, they are paying the lower introductory rates (which is still a lot of money). These people are also more likely to default and stop paying leaving the bank to write everything off. Combine that with the fact that they typically don't spend as much over several years (they hit their credit limit and their income won't allow an increase so they have to stop spending), and they are not as profitable as it seems.