What is it about talking on the phone with telephone companies (or any CSR, really) that makes it so exhausting? Is it the frustration, the trying to get them to do things, and you get bounced between people/departments? I don't recall any particular section being stressful, just talking with people who were helpfully working towards getting things resolved.
My guess is that it you do spend a bunch of energy on trying to elicit support from people. You're watching your phrasing, pronunciation while intently monitoring what the other person is saying because you need to know where exactly they stand. All this, just to get something fixed.