You might want to take a look at Blockstack (https://blockstack.org/). It does exactly this on top of the Bitcoin blockchain. You resolve a globally-unique name to a DNS zone file, which has URI resource records to off-chain data on one or more external storage systems.
Disclaimer: I'm one of its creators.
Would be kind of fun to watch the giants trying to shut it down. Given some level of popularity, it might become too difficult for them to do. Users donate newly minted Google/Microsoft accounts as old ones get shut down. With some sort of karma reward for doing that.