Ignore the expected negativity, many here have not used the latest gen of voice agents in development. Even if used as a router , prefer that to waiting to get through
brutal market for lemons: the last 100 times they heard robovoice on the phone they had a terrible experience, and any money you spend fixing this is wasted because the customer cant tell your robovoice is actually honest and capable of making commitments because they all sound perfectly confident and correct even the ones who know nothing and will promise anything
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+...