Customer support being a bad experience has always to do with the company policies or a general lack of training.
For company policies, an AI would be rigidly trained and limited to always minimize loses to the company, since you can game the AI if it's too lax by saying the exact prompts or keywords.
For companies that do not even provide basic training except for a FAQ sheet, I do not think replacing the human with an AI is going to improve customer experience, because, a human(IC or manager) might be driven by motivation of compensation or job security, to learn more than what is provided, to do their job well.