Camping is a great way to get off the beaten path (even along popular teahouse trekking routes) as well as access more remote parts of Nepal where there isn’t any infrastructure. You’ll have a more unique experience and enjoy vantage points and trails that few trekkers get to see. This is the closest you’ll get to most peoples’ idea of a wilderness adventure. (You can also combine teahouses with camping, as well.)
Keep in mind is that camping treks are often more expensive than teahouse treks as more staff is required to carry the tents, food, cooking fuel, and your personal gear. Some treks also take place in more remote areas, requiring flights and raising logistical costs of access. Still, camping is the best way to experience the Himalaya if you’re looking for a remote and wilderness-based experience.