The amount of storage space you'd need for each car would likely make this too expensive for all but a handful of people.
What you need to know to argue is, say, they're not losing all of the berths on a vehicle transport car if you want to move one car. They're having you pay the upkeep for that one trip which is not the same as the fully loaded vehicle car.
The auto trains that go across Europe are much narrower and take a lot longer to load and unload. They are pretty expensive and only used for very long distances. Most of the time it makes more sense to rent a car at your destination.
Normal bridgdes where? They fit perfectly fine on the French loading gauge (max train dimensions), but the British one is much smaller on most lines.