good question! I've been struggling with it, myself.
The answer is because Satoshi calls PoW a consensus mechanism in the Bitcoin whitepaper:
Nodes can leave and rejoin the network at will, accepting the
proof-of-work chain as proof of what happened while they were gone.
They vote with their CPU power, expressing their acceptance of valid
blocks by working on extending them and rejecting invalid blocks by
refusing to work on them. Any needed rules and incentives can be
enforced with this consensus mechanism
However, the article: A Primer on Blockchain Design states that they are not consensus mechanisms!
PoW, PoS and DAGs are NOT consensus protocols
The much hyped concepts of Proof-Of-Work, Proof-of-Stake and Directed Acyclic Graphs are often mistakenly advertised as “consensus protocols”. Neither of them are, but rather address the key challenges of a robust blockchain design: Sybil resistance and asynchronicity.
This twitter thread explores the idea that we should call them sybil resistance mechanisms:
On Quora: Are consensus algorithms only proof-of-work, proof-of-stake, proof-of-elapsed time etc.?
We can divide the universe into four types of consensus algorithms:
Known participants, non-byzantine failure: Paxos, Raft
Unknown participants, limited attack modes: Chord (original) and other distributed hash tables
Known participants, byzantine failure: PBFT, UpRight, Byzantine Paxos
Unknown participants, byzantine failure: Proof of Work, Proof of Stake, S-Chord
I don’t think that I’ve seen somebody else make the same classification; I threw it together based on examples I was aware of.
I think it is certainly more accurate to view PoW and PoS as components of a distributed consensus algorithms; they are not algorithms in and of themselves.