They aren't robots, they can put on a more genuine tone explaining to the customer that they can't do much, or escalate to someone more powerful without the customer having to argue with them to do it.
A family member had a banking problem last year (they got locked out of their account due to accidentally tripping account theft protection). Of course initially they weren't all that mad, it was their own fault. But customer support staff just had them running around in circles, gradually getting more and more infuriated until one support person finally empathized with their months of daily struggle and bothered to escalate them to someone who was able to force through a fix.
I had a similar experience with my university last year, the support employees were constantly tone deaf about the serious trouble they were causing me by asking me to drop all my other obligations immediately to deal with the consequences of their mistakes.
Every "sorry for the inconvenience" just rubbed salt into the wound because it just further emphasized that they didn't give a shit and that I had no recourse. Especially because the employees did have ways of making things better, by being proactive in providing information and making the accommodation adjustments that were within their power without my having to ask about them.
This sounds like a much broader and uglier problem in the system than empathy between custech and the customer - namely, empathy between the broader company and the customer. I am not convinced that the kinds of companies that will be using these services are the kind of company that even listens to their customer support agents, and would rather sell them out to the lowest bidder and the only reason they have any customer support agents at all is so they don't get in legal trouble because their automated system doesn't have all edge cases supported.
Perfect. We'll just build an AI to translate things into a "genuine" tone for the customer. All problems in society will be solved by adding a layer of AI indirection.