Another aspect of the human version is that the human version is deterministic. Call center workers have a flow that is pretty much a series of if else statements with appropriate edge cases already carved out and places to break out and escalate to another provider. These flows have been iterated over for some time and refined to this point.
AI unfortunately is not deterministic. It would be nice if you could actually use it deterministically in this way, set a seed such that the logic flow are preserved across all sessions well into the future unless the logic flow instructions are changed. They just don't work like that though. Even if you have a good harness they can go off the rails pretty easily and need coaxing to get back to appropriate context. That is a nonstarter for the typical caller of a call center. Functionally speaking just an automated call where you touch type through options would be equivocal to the human operator and that paradigm has replaced a lot of call center work already, with the human operator serving to smooth things over if the person is old or can't comprehend the options for whatever reason and starts yelling incoherently into the automated line (my actual strategy for getting human operators on the line).
Everything becomes a nail though when you have a hammer though, even more so when you are selling hammers. So expect to see AI in plenty of places where it makes no sense to belong given the supremacy of existing tooling. There is also no advocate for a lot of existing tooling unlike AI that has sales teams active in pursuit of new customers integrating this into their product.