Right now, if the internet were to go down, bitcoin would (for the most part) go down with it.
Bitcoin however, can be separated from the internet, and we should probably make a safety net for it.
The next major war will probably involve a lot of cyberwar, and big nations will likely cut of internet of other nations for tactical reasons. For this reason, some organizations have set up their own internet, independently.
Having our nodes interconnected with each other, making our own internet would give many advantages, redundancy only being one of them.
Of course, such a thing has to be decentralized so it would need to be a project driven by the bitcoin community itself, and not a single entity.
If it will be only for the blockchain and the new net will be available and accessible in equal way in all the world it will be a good choice. If the same thing it will be applied in the internet I think that it will be a stupid thing. If every entity or country will have their net the information that everyone will have will be much less than the previous one, the connection between people in two other countries will be more difficult to be realized or even impossible and so on. The world is going toward the integration and the separation. The separation bring only slowdown of development and differentiation. This model it is applied by Kim Jung-Un actually creating an internal internet within the North Korea to separate its people from the rest of the world and, in this way, to control everything they can have from such kind of internet. I thing that this behavior and action of Kim Jong-Un cannot be the example to follow by no one.