This presumes the AI has the same level of problem-solving agency of a real human, which I think is really asking for AGI. Until then I expect AI chatbots will mostly succeed at portraying care and gaslighting customers without actually finding solutions.
Yeah, could be. Most of the time when I contact customer service, there is no problem-solving necessary, and very little agency demonstrated. But I know call centers get a lot of complicated technical or billing questions that would be tough.
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That really depends on the type of call center we're talking about.
Many (most?) call centers won't do much more than telling you to turn it off and on again, even when you're talking to a real person. (And for many cutomers, that is really all they need.)