But the customer will not start speaking before the system prompts them to speak or asks them a question. And since it has to do that in one fixed language, the choice of that language will usually determine what language the customer responds in; this is in the Indian context where most people calling into an IVR will be bilingual at least, speaking English and one regional language.
A not entirely sci fi book plot would revolve around indentured servitude (to put it nicely) what does society and the economy look like after a few generations of only being able to cancel a service if you have more patience and more computing cycles than "the cloud"? As a sci fi plot, what does the world look like when its easier and more likely to kick a heroin addiction than to cancel an old gym membership or cut the cable TV service, or request a credit card chargeback?
Also having a robot repeating: "my customer number is blabla and I would like to cancel my account", "has my account been canceled yet" doesn't exactly take a lot of cycles.
In fact it might be worth it to create cancelation as a service bot, where for a small fee, you can get the bot to call and cancel for you.
What would the benefit be? Of course the customer will gain a few seconds but I don't see a large improvement.