I think it all depends. I had a mobile service appointment last week. It was set up quickly and easily. They damaged my door replacing the sensor. They scheduled another repair for today.
Repair guy couldn't get behind the door sensor to fix the dent. I just texted the person who was in charge of mobile service who reached out to me and she (granted this is lucky, but this shows how responsive they can be) contacted one of the mobile guys who was in the area. They got a Lyft out to my house with some tools to take apart the door panel so the dent repair guy could fix the damage. During the install, a second tesla guy came to bring more tools in their model S vehicle. They were still missing parts and they had a third part dropped off within 15 minutes (granted the service center is less than 10 minutes from my house). The entire fix took three of their guys but they were EXTREMELY responsive.
I think it's unfair to say that, across the board, they're totally unresponsive. Maybe I've been lucky, but I've always had a pretty darn good experience from the initial ordering with my through delivery and all warranty work I've had to do.
Just thought I'd chime in on a positive experience to at least prove that they can be extremely responsive and helpful too.