You might be underestimating just how many ships full of cars there are? The port city where I live has ships doing this all the time, there are literally rail

You might be underestimating just how many ships full of cars there are? The port city where I live has ships doing this all the time, there are literally rail shuttles moving hundreds of vehicles from outside the city to the port sometimes several times per day and some of the huge carparks in the restricted dock area are dedicated to parking vehicles ready for export until a vessel arrives to take them.