I noticed Autodoc offers use of trailers at his facility, click on his webpage link in his signature. I'm sure he has some insight into trailers. I'd be a little concerned about a trailer, in many respects they are harder to handle than a 14' moving van. Most people have no idea how to back up a trailer. I would also be concerned as to who actually does the hookup to the customer's car. If you or one of your employees does it, I assume you take on some liability for doing it safely and correctly, and knowing whether or not the car is appropriate for pulling that extra load. If you have them do the hookup, likely many will have no idea where to start.....ball size, safety chains, light hookups, how to distribute the load, tarping, securing, etc.
In my market I have to fight with a truck, since that is what the standard is now. A trailer would do nothing more than make people laugh at me

I would guess there is some measure of insulation liability-wise with a truck too, since they present a valid license that says they are qualified to drive a vehicle of that length and size. You wouldn't get that type of assurance that a customer knew how to handle a trailer from looking at their DL.