The phone system was a great in some ways. Humans to talk to! However it was supposed to be for Billing, Account Access (passwords. email change, country change, etc), and some tech support.
BUT people called it for all manner of reasons. To submit suggestions, to ask for game hints (Not something GMs are allowed to do), to complain, to appeal bans, to get a GM joke, etc.
End result is it clogged up the lines. Getting into the queue meant redialing many many times, then the queue was 2 hours long. Enter cell phones. They did not like to be on hold and disconnected. Further, it eats minutes being on hold.
End result, they got rid of the dial in and set up a triage system.
They DO have Live Chat and Phone Callback but only for the issues that are supposed to be handled by them.
CS does not support just WoW. They take tickets from every Blizzard game and service.
A better idea of what GMs can handle you can read up on what GMs can do, and can’t do.