All Proof of Work is useful to those who pay for it. Proof of Work does not reward "the most wasteful" producer, if that were true a bitcoin miner [A] with an inefficient HVAC system, who leaves the lights on, and has chips with copious amounts of Joule heating would be rewarded more than a [b] lean PUE, capitally-efficient miner which we all know is not the case.
Producing digital "fraud armor" is valued by systems that can only rely on digital verification in Sybil-attack prone networks (aka the entire real-world environment where one needs to interact with entities outside of a trust circle). Be wary of old, dated, reductive, "small game" arguments that laundering the fraud/security costs of vetting to other systems and then exclude those vetting costs; they don't count as "being more efficient".
You likely encounter fraud Proof of Work but that you have no option but to trade your valuable brain time. A Captcha is a fraud and congestion control mechanism. PoW critics claim that since they push all of the verification costs from the center to the clients that it's an efficient solution (when likely most would use reusable value to avoid the captcha -- say a money).