Training is more stable and faster when parameters are small. As a fact, none of these first order optimization method guarantees finding minimum for arbitrary network (in fact, they can’t even find it for the simple ones). Therefore, although scaling & offsetting is equivalent to scaling the weights and offsetting bias at first linear layer, normalization proves to often give better results.
Moreover, you shouldn’t normalize using every pixel’s mean and std. Since conv is an operation on channels, you should just use each channel’s mean and std.