Though privilege is multifaceted and Katara, Sokka, and Aang all had certain advantages in their world, it’s hardly fair to claim they’re rich. Katara and Sokka may have been the children of the chief, but their village was tiny and isolated. Their father, and most of the village, also left when they were quite young after they were attacked by the Fire Nation. When we meet the two in the present, it’s clear they’re not living a life of means. What’s more, they are clearly outsiders in the wider world, which is predominantly made up of people from the Earth Kingdom and Fire Nation. Even in the more affluent Northern Water Tribe, they’re treated as lower-class outcasts.