The promise of this work is that we can have fully connected nets 30 layers deep, or more. Up until now they didn't work for more than 2-3 layers in depth. The fully connected nets have been untamed and wild until now, but now they can be made to behave.
Now that it has been shown to be possible, in a few months we could see more solutions.
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?
> Both RNNs and CNNs can stabilize learning via weight sharing, therefore they are less prone to these perturbations. In contrast, FNNs trained with normalization techniques suffer from these perturbations and have high variance in the training error (see Figure 1).
Essentially FNNs stand to benefit more from this work than CNNs or RNNs.