SEOUL—An international operation to take down what was the world’s largest child-pornography website resulted in heavy prison sentences around the world—but not in South Korea, where much of the material was uploaded and viewed.

The 23-year-old South Korean man convicted of creating and running the website received an 18-month prison sentence that will soon run out. Scores of people who were convicted outside South Korea of using his site were sent away for much longer. One man in the U.S. was given a 10-year prison sentence...