GAN - why doesn't the generator nullify the noise input?
If the generator always outputs the same image, then it's easy for the discriminator to win the game and tell apart the output of the generator from random images in the training set: if the input to the discriminator is that one image, then it outputs "came from the generator", otherwise outputs "came from the training step".  The game is set up so that the generator is rewarded for fooling the discriminator.  Always outputting the same image isn't going to fool the discriminator.