You see, the cost of buying rights to licensed characters and TV shows, some of which would be canceled before the box had a chance to sell, was becoming astronomical. Aladdin decided to create some generic-subject boxes and decided the new shape would be a novelty selling point. Its artists rose to the challenge, given a bigger canvas and freed of the tyranny of having to please temperamental producers and stars (Rex Harrison, for example, bounced the art for the Dr. Dolittle box six times before okaying it).
Aladdin's first dome, "Buccaneer" in 1957, capitalized on a pirate craze that had been spurred on by Peter Pan and other movies of the era. It was a huge success. From there, domes featured other whimsical patterns, some of which like the VW Bus and the Disney Schoolbus, which at 9 million units was the biggest seller of all time used the shape of the boxes to brilliant effect.