Maybe I'm missing something, but this doesn't feel like an improvement over customers having my personal phone number. I understand providing good support is important, but being able to step away from unnecessary contacts and work in your personal space when you are up against deadlines / emergencies is something I value more than being available for a customer.
This rant really only applies to the suggestion of using a chat client - the interface to see their customers' pertinent information (logged in, pages browsed, location, unique visits) does look very helpful.