The DNS is like the Blockchain a distributed database. DNS stores meta data about domain names (IP addresses and other meta data, for example Sender Policy Framework to make e-mail spoofing difficult).
The Blockchain is a trustless ledger. Trustless means that nobody needs to trust some authority about the trueness of data. Blockchain can store any data the people want. In Bitcoin’s case it’s money (but also arbitrary data is allowed).
DNS started without security. Later came DNSSEC, the security extensions, to ensure integrity and authentication but not availability. DNSSEC is still not implemented everywhere today. DNS is an old protocol from the eighties, however the core invention is still unique and important today: a simple and efficient distributed and also hierarchical system of providing information.
Blockchain has a distributed system of providing information, too, a peer-to-peer network. This system guarantees availability (something which DNS lacks). The US could censor DNS but not a Blockchain. Theoretically.
There are many peer-to-peer network implementations, like Kademlia, the distributed hashtable implementation of Bittorrent. Everybody can connect to such a network and manage data. Central servers aren’t required, so they can’t be shut down by the government or catastrophes. Bitcoin uses its own different implementation.
DNS doesn’t peer-to-peer.
First DNS uses many servers. If a server doesn’t know about a domain, the server asks a different server for information.
Second the data is structured hierarchically. Not only there are so called roots, but the responsibilities of the data is also structured hierarchically. If you own example.com, you can manage subdomains of example.com yourself, but not the top level domain .com.
There’s NameCoin which provides an alternative DNS based on Blockchain. This proves that it is possible to manage domains with a Blockchain. However the responsibilities must be also hierarchical. This is an inherent requirement of a recursive name system.
So it’s a bit arguable whether NameCoin is Blockchain or DNS or both. It’s an ontological question. In other words: if you have something can you call it such or such?
But practically the answer is yes, a Blockchain could replace DNS!
But don’t open the engine hood or you will be surprised what is there.
DNS could be replaced by Blockchain as NameCoin proved it. However as everybody talks about DNS implemented by a Blockchain, we see we are comparing apples with oranges. Somewhat.
At least the damned thing drives whether it’s on electricity or gas.