Customer service handles all the things that customers aren't trusted to manage on their own with a self-service portal - that's the whole point of having a trusted human involved at all. Giving those tasks to LLMs won't work because the customer can just prompt inject their way to whatever toolcalls correspond to their desired outcome.
Five years ago, you'd wait on-hold to talk to a human being with a script. "Is the light on your modem red?" "Try turning your modem on and off again." "OK let's schedule a technician for you."
Today I get a pre-LLM chatbot, with the same script, no waiting on-hold, available 24/7, with pictures and guides. It's somewhat faster because no human has to read the script over the phone, the words just appear instantaneously. Getting through the script tree to the outcome I want is an easy and obvious path.
The vast, vast majority of Tier 1 support is not something where the customer service agent has any agency. They have a script. Taking humans out of the loop here is an improvement.