Yup. I'm pretty good at avoiding talking to people, yet I've needed to call in a few times recently for stuff I should've been able to handle online:

• report fraud
• cancel credit card
• report internet outage
• buy insurance

If they want to save money on customer support, make the customer support less necessary to get routine tasks done...

The thing is, I rarely want money from them, I just want to provide them information to make my experience as a customer better. For example:

• my card kept getting declined, so I wanted to help their investigation by flagging fraud
• close a credit card - feel free to show me retention offers and whatnot, I'm more likely to accept online than over the phone
• report an internet outrage and see whether there's a known outage - I actually can make a report, but they've never followed up, so calling is the only way to make sure they actually got it; I just want to know that they know about it

I can see a reason for the credit card thing sucking since they want to make a bad offer and keep you as a customer, but at least for me, all of the above would make me more likely to stay a customer instead of switching to a competitor (and I've seriously considered switching each of the above).