Because standard linear smoothing (like averaging) tends to filter noise but reduces the contrast. Image composition is not often linear: cast shadows, occlusions. So linear methods tend to be suboptimal.
When you want to preserve sharp contrasts, for instance with multiplicative noise (whose intensity varies with image intensity), when you have a slow variation of the global illumination across the image (like progressive shadowing effect), when you want to both denoise and enhance
Images taken under varying illumination conditions, with noise varying with intensities, for instance related to temperature (infrared, visible of hot objects).