There are different levels of inoperability. The first level is where your car starts and can be driven onto a trailer but driving it anymore than that will cause damage to the vehicle or would be impossible. This kind of vehicle is usually not an issue for carriers. You may pay a little but more but if the car can go up and down the trailer under it’s own power then some carriers may not even consider it an inop.
The next level is where the car simply doesn’t start. At this level the car will roll on and off of the trailer and the only damage is mechanical. At this point shipping your car can get expensive. The carrier will need special equipment or you will need to provide the equipment to get the car loaded and unloaded. Some carriers have a winch on their trailers which is used to pull a car on. At drop off the car either gets rolled off of the trailer or is pushed/pulled off. Other options for loading and unloading the car would be a tow truck or a forklift.
The third level involves damage to the body of the vehicle. These vehicles have bent axles or bent frames or even missing tires that prevent them from rolling freely. A forklift will be required to load and unload this kind of vehicle, because a forklift is something that you must provide the cost to ship is usually not too much higher than cars at the second level.
The final level would be a car that is so destroyed that you can no longer even call it a car. This could be a car that was burned and just the frame is left or maybe even just the front half of a car or whatever else. Auto transport carriers are not equipped to transport these kind of vehicles. Technically their insurance does cover it but in reality securing a vehicle like this is a job that would be performed best by a flat bed trailer.
Cost to transport gets higher and higher as you go up the levels though there is some variation. Auto transport demands very specialized equipment. Car haulers haul cars and only cars. The way trailers are set up is truly for running automobiles and transporting anything else with that equipment is difficult. The more difficult the job on your driver the more expensive it gets on your end.