A few days ago, it was reported that Julian Assange "read out a bitcoin block hash to prove he was alive". This was in response to rumours that he had died. It was a neat demonstration not only that he was not dead, but also of a couple of limits to the blockchain that are still not widely appreciated. It showed that blockchain on its own provides little value beyond cryptocurrency; in particular, on its own, blockchain doesn't 'prove existence'. And further, we can see that when blockchain is hybridised with other security processes, it is no longer terribly unique.
What Assange did was broadcast himself reading out the hexadecimal letters and numbers of the most recent block hash at the time, namely January 10th. Because the hash value is unique to the transaction history of the blockchain and cannot be predicted, quoting the hash value on January 10th proves that the broadcast was not made earlier than that day. It's equivalent to holding up a copy of a newspaper to show that a video has to be contemporary.
With regards to proof of existence, the evidence on the blockchain comes from the digital signatures created by account holders' private keys. A blockchain entry certainly proves that a certain private key existed at the time of the entry, but on its own, blockchain doesn't prove who controls the key. A major objective of blockchain as a crypto-currency engine was indeed to remove any central oversight of keys and account holders.
Quoting the blockchain hash value from January 10th doesn't prove Assange was alive that day. It is the combination of the broadcast and the blockchain that tells us he was alive.
If this is an example of blockchain providing proof-of-existence (or "proof of life" according to some reports) then the video is like a key management layer: it augments the blockchain by binding the physical person to the data structure. Yet the combination of a video and the blockchain doesn't provide any unique advantages over, for example, a video plus the day's newspaper, or a video plus a snapshot of the day's stock market ticker tape or lotto numbers.
The pure blockchain was designed to manage decentralised electronic cash and it does that with great distinction. But blockchain needs to be combined with other processes to achieve the many other non-cryptocurrency use cases, and those combinations erode its value. If you need to wrap blockchain with other security mechanisms to achieve some outcome, you will find that the consensus algorithm becomes redundant, and that simpler systems can get the job done.