Consistency of interface. I've got the phone number of the mechanic I go to in my phone's address book... and the various medical services for appointments there.
If they were to have an app on their website, I wouldn't know because I don't use the webpage for that purpose - I call them.
Now, they've all got receptionists there that work full time and handle the appointments and take that first tier of service. These are larger places that have two receptionists working the full day (handling walkins, calling confirmations, and the other administrative tasks)... I don't think that an LLM (even with access to appointments) would do a better job than what they do (and certainly wouldn't be able to do the "ok, I showed up, now what do I do?")
However, I could see this for a small mechanic shop. When I lived in California, I went to what is now Shoreline Auto Care on El Camino and Shoreline - a small two bay mechanic... and that's not the type of place that has the business that can afford a full time receptionist.
So the question for a place like that... "what do you get for the phone calls you miss?"