What would we do if an attempt by hackers or an enemy state to take down the internet would succeed? Even though the internet is essentially a huge decentralized network of cables, the DNS structure is not so decentralized and has already been target of attacks. Even this week, a distributed attack on Dyn's DNS caused many US visitors unable to reach popular sites like Twitter and Github.
There are also governments that censor sites like Twitter and Google for political reasons. People have a natural wish to share information, and this question is really about how this can be facilitated when common social network sites are down.