I looked at that account today, and it was time to pay the annual fee. I couldn't see paying $60 for a card I never ever used, so I called to cancel the account.
I got a real person very quickly, authenticated myself, and stated my business, at which point their sales pitch began.
Why do you want to cancel this card? (I haven't used it in months.) But you've had this card for years, and it's probably one of the most valuable items on your credit record. (I don't care.) We'd be happy to cut your annual fee in half for this year. (I can't see paying an annual fee for a card I'm never going to use, when I have cards with no annual fee.) The cards with no annual fee get you in other ways. For example, they may calculate interest in this scary-sounding way rather than our way, and it can cost you hundreds of dollars a year. (I don't carrry a balance... I don't care. And even if I did carry a balance, I'd do it at far less than your 15.6% rate.)
She tried several jedi mind tricks to try to convince me that it cost me more money to have other credit cards than this one did, at which point I decided to just lie to shut her up. "Look, I have a masters degree in math; I understand compound interest."
I think that intimidated her a little bit, because she stopped trying that degree of persuasion, but it still took another few minutes to actually get to the point of closing the account.