Depending on the kind of chat system they could be very useful in the banking sector.
The simplest chat-like system implement would of course be one that simply works off of a flow chart of responses, in which case it’s just a presentation layer guiding people to an item. I would argue though that those types of systems aren’t really chatbots, since you aren’t actually chatting! However, I do think that this kind of system could be useful in a banking situation, since the “domain” size is fairly limited in scope and thus this would be easiest for both consumers (since they can’t confuse it) and developers (since it doesn’t have fuzziness)
A chatbot would have to be something you could converse with in one or two short sentences. I don’t think the domain of banking is large enough for this kind of system though.
I guess you are more thinking of a blend of the two? Like a system in which I could type “I want to know about credit cards”, or “What is a credit card”, and it would pick out the terms “credit card” and “what” and respond with something about how a credit card works?