> The granddaddy of all consensus mechanisms—behind Bitcoin, Litecoin, Monero, and (for the time being at least) Ethereum—is called proof of work. Essentially, PoW makes adding transactions to the blockchain computationally—and therefore financially—very expensive, so as to discourage fraudulent activity. ...
This passage reflects a deep-seated, widespread misunderstanding of how/why Bitcoin works. I suspect the author knows, but the brevity of the article prevents actually explaining the issue. This is a recurring problem in this space and has opened up a large fraud opportunity as every bottle of snake oil looks the same to those who don't do the deep technical dive.
Proof-of-work has nothing to do with ensuring the validity of transactions. Transactions contain all of the information needed to detect invalid transactions. Hashes, signatures, scripts, and amounts can all be checked and will be rejected if invalid. The validity of every transaction can be tested without proof-of-work. Systems like this had been developed prior to Bitcoin.
So it's possible to eliminate every kind of fraud through cryptography alone, except one.
The problem proof-of-work solves is double spending, a term you won't find in the article. A malicious actor can try to spend the same coin twice (or more). Both versions of the double spend transaction are valid, but a node can only accept one. Which one does it accept? It accepts the one on the block with the most cumulative proof-of-work ("strongest chain"). In the event of a tie, the node accepts the first version it saw. The strongest proof-of-work chain can therefore change from one moment to the next as blocks are received.
Proof-of-work imposes a non-recoverable cost to publishing a block of transactions. That cost and its finality discourage double spending by making the publication of double spending transactions permanently expensive. An attacker needs to out-spend the entire rest of the network to succeed, and loses everything spent if the attack fails. The cost of a failed attack can never be recovered.
So any scheme to replace proof-of-work needs to maintain that element of irrecoverable loss of value for a failed double spending attack. It hasn't been an easy nut to crack. A lot of projects claimed to have done it only to discover some flaw in the game mechanics or technology.