SOUTH EUCLID, Ohio -- Parents and grandparents of small children are likely familiar with the animated series “Paw Patrol,” in which a boy named Ryder leads a crew of talented search-and-rescue dogs.

When my son was a baby, I swore I’d never let him watch PAW Patrol. At the time, I thought of it as the kind of TV show I didn’t want my child to become obsessed with: noisy and overstimulating. But ...