I'm not sure if this would pass a security review, but occasionally I've had some issue with a bank or credit card account, I've then used the chat-based technical support, and the conversation was very straightforward.
I could definitely see chatbots becoming advanced enough to handle "I'm locked out of my account and need some part of it reset" type questions within the next 3 - 5 years. I could even see it being superior to the current experience (right now there are significant delays after each thing I say to the customer service person, presumably because they're handling multiple chat windows simultaneously).