No I didn't prove your point. Private key signatures are a fundamental component of blockchains. Without them blockchains cannot function.

I figure this will probably be a lost cause but let me try to explains some basics about "blockchain". I'll be focusing on Bitcoin specifically since that's what I have the most knowledge in but every cryptocurrency is based in some part on the way Bitcoin works.

The blocks in the chain are comprised of a series of transactions. The first transaction being the coinbase transaction which is the reward miners receive for mining the block. This transaction is unique in that it has no inputs. All other transactions will have inputs with a total balance greater than or equal to the outputs. Any leftovers are also given to the miners as a mining reward. Transactions are verified by miners using private key signatures. Each input is accompanied by a signature proving the inputs are being spent by the individual or group who owns those inputs. Once all transactions have been verified by the miner and the coinbase transaction has been created the miner sets about to mine the block. They do this by hashing the entire block and hoping for a result that comes underneath the value of the mining target.

I can go into more detail on any aspect of this. But what I'm mainly pointing out is that private key signatures are not something external. You cannot have a distributed ledger without some mechanism for proving ownership. Otherwise anyone could spend anybody else's bitcoin. You can leverage other pieces of data contained within a transaction output to represent other information such as the hash of a digital content like an image. An owner can cryptographically demonstrate they have the ability to spend an output without spending it. Thus demonstrating they own digital content which hashes to that value. You can do this with pictures, movies, music, books... whatever.

And frankly, that's the boring part of the capability. Cities and counties could use hashes of deeds or full text of deeds themselves to represent property ownership. Essentially placing the burden of backups, redundancy and lookups on the decentralized nature on a blockchain. This opens the door for better interconnectivity between the way various government bodies track ownership of things like land, homes, cars and whatever else. All this information is already public and stored digitally but the money spent on creating and maintaining these individual systems is incredibly wasteful. The lack of consistency also creates problems in legal spaces.