To get rid of search engines like Google and Bing we don't need to build a new internet - we just need to build new search engines.

E.g., how about an open source spider/crawler that anyone can run on their own machine continuously contributing towards a distributed index that can be queried in a p2p fashion. (Kind of like SETI@home but for stealing back the internet).

Just think about all the great things that researchers and data scientists could do if they had access to every single public Facebook/Twitter/Instagram post.

Okayokay ... also think about what Google and FB could do if they could access any data visible to anyone (but let's just ignore that for a moment ;)