What do land titles, marriage certificates, diamonds, ballots, aircraft parts and medical records have in common? They are all apparently able to be managed "on the blockchain". But enough with the metaphors. What does it mean to be "on the blockchain"?
To put a physical asset "on" the blockchain requires two mappings. Firstly, the asset needs to be mapped onto a token. For example, the serial number or barcode of a part or a diamond is inserted as metadata into a blockchain transaction, to codify the transfer of ownership of the asset. Secondly, asset owners need to be mapped onto their respective blockchain wallet public keys (through the sort of agent or third party which Nakamoto, let's remember, expressly tried to get rid of with the P2P consensus algorithm). The mapping can be pseudonymous, but buyers and sellers of land for instance, need to be confident that the counterparties control the keys they claim to.
How does the "naked" blockchain get away without these mappings? It's because Bitcoins don't exist off-chain. In fact they don't exist "on" the chain either; the blockchain itself only records subtractions and additions of balances.
Furthermore, possession of the private key is the only thing that matters with Bitcoin. Control a wallet's private key and you control the wallet balance. The protocol doesn't care who is in control; it will simply ensure that a quantity of Bitcoin will be transferred from one wallet to another, regardless of who "owns" them.
So unlike any other cryptographic security system, Bitcoin key pairs need not be imbued with any extrinsic significance, or associated with (bound to) any real world attributes. Bitcoins have no symbolic meaning. And in fact that is blockchain's magic trick!
But to make tokens stand for anything else - anything real - breaks the spell. Symbols are defined by authorities, and keys and attributes can only be assigned by third parties. If you have administrators, you just don't need the additional overhead of the blockchain, which exists purely to get around Nakamoto's express assumption that nobody in his system of electronic cash was to be trusted.
Bitcoin is often said to be anonymous, but its special property is actually that it has no meaning. It's truly amazing that such a thing can have value and be relied upon, which is a testament to its architecture. Blockchain was deliberately designed for a non fiat crypto currency. It's brilliant yet very specific to its intended trust-less environment. To re-introduce trusted processes simply undoes the benefits of blockchain.