I have a somewhat similar problem with British Gas; my wife does not want to be an "On line" customer and send readings in case, one day, I am not around. When they ask for a reading by e mail format and you try to reply "I am not an on line customer" it gets rejected.
A month or so ago I had a problem with BT e-mail, so I used an alternate e-mail address to report the issue. Their response was to send an e-mail me to the address I couldn't access a request for a phone number so that we could "fix the issue by going through voice interaction" Fortunately the problem went away thus allowing me to savour their rather stupid request.
Before I retired - 17 years ago - we had a 4 screen workstation which had a key on a single keyboard to switch between main frame, PC and Reuter. The other screen was a touch screen telephone and we had headsets and could use 2 telephones. I am not sure if , these days, such a (simplified) touch screen telephone system is available but I can imagine some issues that may preclude speech as a medium.