I was agreeing with all the nay-saying comments, but yours made me see the idea as good. I guess the word "luxury" ruined it for OP.

But a speech-to-text and text-to-speech system that I know is "understanding" me would be great rather than waiting music. The shop could even sell it as "As a small shop, most of our employees are busy fixing cars, so we are using AI to help with calls" (Although then people who are anxious about AI stealing jobs might hang up). The robot can ask me what I need, and then say "So for [this service], the price would be..." (to tell the caller what it has understood).

If the AI can even look at gaps in the shop's schedule and set an appointment time, the customer might even be happy that they just spent a minute on the phone instead of 10+...

I would rather just be sent to a regular old answering machine. Dealing with an AI is dehumanizing. In almost every single case where I actually need to call a place, its because I need to talk to them about something an automated system like booking an appointment, can't handle.