Why is the cost of shipping an SUV more than a car?
Car carriers can load only so much weight and so many cars at a time based on the weight. The size of the vehicles will also affect the limit of that available truck space.
An SUV uses up more of the allowed wight. SUV's are also generally larger. So, the carrier will be able to carry less vehicles on it. So if your 8,000 pound Escalade ESV will shrink the load space available by both weight and size.
As the carrier selects what they want to take, they will want to get more money for bigger vehicles so they can make what they expect to make for the route.