I work for an IT hosting and service provider. We calculated that if we get a customer contact then it costs on average about $10 to handle it, but this is only achieved when there is an optimized and even load on the Helpdesk. If you were Amazon or Google and get those massive problems with suddenly millions of people not getting their service you just could not handle them with traditional Helpdesk (e-mail, phone, chat) support...even if you outsource it to India.
So something else is needed, but can be done.
Another important factor of customer support is that people are always much more patient if they know what is going on and when the service is expected to be OK. This is the "lift effect".

If you get a chance examine people waiting for lifts that have dashboards showint the floor the lift is currently on and to what direction it is moving. They wait for it calmly, sometimes cursing, but still calmly. Whereas with lifts that don't have those dashboards...well their call-buttons get a lot of pushing.