Do what a few providers already do. On calling, the automated system asks for the telephone number of the line you're calling about, then asks for your PIN. It then transfers you to customer services.

There's a big difference between being accessible when needed and accessible at all times.

Pull up the data on the caller as they call? Call centre staff don't need access to my details unless I'm on the phone to them, or I have a case open that they're still helping with.