The shorter version comes down to a number of key reasons:
1. We can't satisfactorily authenticate you as the account holder (and confirm that you have access to the account) over the phone. We have to do that for security before we can make any account changes.
2. We might need time to investigate or escalate the issue, so keeping you on hold won't solve things any faster. (Just getting a person on the phone doesn't make issues easier to fix, unfortunately.)
3. Online support keeps all the information about your issue in one place. We can also connect it with previous cases we've worked on for you to see if there's a recurring thread or something that's changed, or escalate it more directly to the developers.
4. A lot of our responses contain URLs, IP addresses, or other complex information. That can't be accurately communicated over the phone, plus it saves you having to try to type in some long web address we dictate. Email also lets us include screenshots or even video to be clearer.
5. People are often not very good at describing their problems, simply because it's not their job to have a deep understanding of the systems in question. That is our job, so it's more efficient for us to look at the account, records, etc. directly rather than get a description.
6. Not all phone networks are created equal, especially in an increasingly mobile world. If we can't hear each other, we're not going to be able to sort out your issue very effectively.
Customers can help by providing as much specific information as possible, and sending an authenticated request, which enables us to do more for you more securely. Login to your account, then go to our support form and send us a message from there.