Internet is already decentralized
And it is conceptually decentralized. While you would have to use the DNS system to access sites using their mnemonic names (e.g. bitcointalk.org), which can be considered as some form of centralization, you can still access the same site in a completely decentralized way using its IP address. You just need to know this address, which loosely matches a wallet address in Bitcoin, as well as the IP address of your gateway. The latter can be construed as a mining node of sorts confirming your request and sending it to its own gateway or directly to the site if it is a gateway to it. Note that you don't have to pay any fees for sending and receiving network requests, and the same should be done in Bitcoin in regard to transactions
It could be seen that way, although
it is somewhat centralized in the sense that governments could shut down a specific site, as well as ISPs being able to censor access to certain sites. However, with a fully decentralized internet powered by the blockchain, it would make it harder for government agencies to take down any site, as the same would be replicated across all the nodes on the network. I know that it may not be the most viable solution for large sites, as the blockchain data would become even bigger than Bitcoin's, but as storage capacity increases over time, it may become a reality at some point in the future
If we accept this point, we could then just as easily claim that Bitcoin itself is "somewhat centralized" because governments can shut down a Bitcoin node or a mining farm. The whole point of decentralization revolves around resistance to such actions, i.e. shutting down one site or node doesn't shut down the whole system. Apart from that, it is pointless to replicate a site (or whole Internet) over blockchain (somehow else) since if the resource gets closed or access to it is blocked, its copy could be launched elsewhere in less than no time