It actually costs banks money for you to have an inactive account. Credit cards are considered variable draw unsecured loans and are subject to the highest capital ratio of 100%. They have to retain capital to the tune of 100% of the their retained capital level which is somewhere in the 6% range. So if you have a $1,000 limit with a zero balance they have to keep approximately $60 in retained capital to cover future losses.
That is money that cannot be invested and is otherwise costing them in terms of lost revenues and unearned interest.
It's a business proposition.
To the guy that claims he doesn't buy anything on credit. You're in all liklihood doing yourself a great disservice. Properly leveraging your finances is the most profitable way to use your earnings and savings. In addition you have liquidity risks that you haven't priced.
Tom