Proof-of-work was created precisely to prevent a Sybil attack, but while allowing an open network (i.e. not having to buy the token from the creators).
You need a form of scarcity to prevent a Sybil attack.
Solved cryptographic puzzles of an adjustable difficulty is one such form of scarcity.
Proof of work, it’s inefficiency, or it’s security implications on transactions more generally are not relevant to your comments on the vulnerability of their coin faucet or the veracity of their claims.
They related these two points by saying that either it’s hackable, or there’s something weird going on under the hood, and that proof of stake alleviates these issues. Idk if I agree or disagree but it seemed straightforward and relevant what they were asserting.
There were three concepts being conflated in the comment I originally replied to: Sybil attacks, double spending prevention mechanisms like Proof of Work and Proof of Stake, and exactly-once delivery to members of a group (i.e. what a coin faucet does and the creepy biometric privacy destroying Orb thing TFA reacts to). TFA discusses an identification problem, and how this particular solution is creepy and privacy-destroying.
A Sybil attack is a single or a small number of entities counterfeiting multiple peer identities so as to compromise a disproportionate share of the system. The actual network of communicating nodes that have copies of the distributed ledger (whether they be participant wallets, miners, validators, stakers, or any other kind of node), and the append-only list or tree of wallet-to-wallet transactions (i.e. the distributed ledger) are distinct, and may be what's tripping up some.
Within that distributed ledger, proof of work or proof of stake aren't what prevents the Sybils from using your (or others') identities on a cryptocurrency's network without your private key. Transaction signatures alone are the mechanism that prevents impersonation. Sybils can flood a cryptocurrency network with transactions with fake signatures all they want, but the transactions would be invalidated the moment that any node appending to the distributed ledger attempts to verify those transactions against its copy of the blockchain or ledger. In Bitcoin's case, the wallet address is the public key for that wallet, and the transaction signature is easily verified by using the source wallet (the one that has a balance) address as the public key for signature verification. (The wallet address is a hash of the public key, and I'm oversimplifying.)
The function of Proof of Work is to mitigate double spending by the same identity, which is a different concept from a Sybil attack, and is not even a type of Sybil attack. That double spending would otherwise "fork" the distributed ledger, and cause two different parallel versions of the distributed ledger to exist - one in which the destination wallet A has the transacted coin, and another in which the destination wallet B has the transacted coin. The iterated game miners play in PoW makes it computationally infeasible for a single party to double spend without controlling more than 50% of mining (e.g. hashing) power in the communications network of participating nodes. In the case of Bitcoin, for example, spending the same Bitcoin wallet balance twice by signing two different transactions using the same wallet private key. That is not a Sybil attack because the double spend (i.e. both transactions) originate from the same wallet. Double spending by a single identity is irrelevant to TFA, and not what TFA is talking about.
TFA responds to a coin faucet proposal (Worldcoin's "Orb" mechanism) that uses a biometric challenge to verify that coins are distributed to flesh and blood humans only, and exactly once. They're mitigating an identity problem with coin faucets, not an integrity or double spending problem that Proof of Work mitigates. (And in a creepy, biometric privacy destroying way, we'll get to that later.)
Coin faucets can be used to give some value (e.g. a small amount of cryptocurrency) to as large a population as possible to enable, for example, developers to play around with the cryptocurrency and new users to try it out before buying in with their own money. The referenced coin faucet is proposed as a wealth (re?)distribution mechanism. Currently, coin faucets mitigate a single or small number of individuals from consuming all of their cryptocurrency by restricting IP addresses, browser cookies, wallet addresses, and other forms of identification. The "Worldcoin Orb" hardware device for that identification collects biometric information (i.e. facial recognition, eye recognition, etc.) centrally to ensure that only flesh and blood humans receive the initial grant of their cryptocurrency. One of the comments here previously mentioned that you might be able to just spoof the output phashes of these "Orb" devices to perform a Sybil attack on the coin faucet in TFA that uses biometric phashes.
Hopefully this helps explain why this type of Sybil attack is distinct from attacks on the proof of work or proof of stake mechanisms, such as owning 51% of the mining power on a POW network or all the validators on a POS network.
As an aside: An encoded, encrypted, or hashed version of your biometrics that can be used to identify you from those biometrics is still biometrics. As long as it is generated from the source material, and uniquely identifies an individual, it's still biometrics, and still creepy facial recognition, IMO.
Just wanted to say I really appreciate this long and thoughtful response - and sure you are probably proving the OP wrong, I just don't think that what they wrote was inconsistent, even if it turned out to be wrong.
In this case, there are 2 graphs/networks (3 if you count the "Orbs"), 3 different kinds of Sybil attacks, double spending, ECC signatures, and more. It's easy to lose track. I wrote it to check my own understanding.
Justifying the use of proof-of-work appears to be a fallacy of relevance though