On principle you're right, but at least for computer vision the number of layers you mention are a bit off. VGG16 worked well with 16 layers without any special handling. ResNet went to >150 layers by using shortcuts, which kind of cracked the problem already. This paper gives us more insight and maybe a more elegant solution.

edit: Just realized you said 2/3 _fully connected layers_, which is right. But for convolutions we needed skip connections, too, to get them to work. Any reason you single out fully connected layers?