# Why are weights not initialized with mean=1?

I wonder why weights are initialized with zero-mean. It is one of the reasons, why deep architectures cannot be trained without skip connections. Without the skip connections, the zero initialization becomes problematic, because the identity function cannot be learned in earlier layers (this is a simplified explanation I know). But why can we not initialize weights around one? This would enhance the intrinsic learning of the identity function. Of course, the skip connections also allow a better backpropagation of the gradients, but couldn't this be helpful anyways? Can anyone tell me, why this is not done?