Information bottleneck and deep neural network

I learned about "the information bottleneck view of deep learning."
But in a nutshell, what does this tell us?

I don’t see what the role is of depth in this approach as long as it is larger than 2 or 3.
Is there a rigorous theory? Or just some hypothesis or heuristic explanations on deep neural net?

I saw the author’s talk on YouTube.
But, probably my ignorance, I don’t really get the main point and the implication is.
I can see a lot of explanations on graphs on the video, but honestly, I don’t get it.

Any comments, suggestions, opinions will be very appreciated.