Not yet. People tried it.
- They introduced TOR for user privacy still it's centralized but protects user identity.
- Torrents for file sharing. It's going well.
- And now Blockchain for totally Decentralized internet. Have to wait for it to see the results.
Actually you can host your own web page at home, and serve it thru tor as a so called "hidden service" (.onion address). It is quite safe. Torrents, not so much. Blockchain is a type of decentralized unalterable write only database, its not exactly an "internet replacement", but quite useful.