I can tell you this: it's much more efficient to do support via email/online. If I were to do it over the phone, once lizzie calls me, i'd b tied up chatting with her for the next 6 hours. I'd enjoy the experience but would never get anything else done.
Online though, I can chat with lizze for 6 hours and get everything else done at the same time.
Also, many of our support tickets require research, replies from other members of the team, escalation, etc...