You're technically correct in that it does provide some value, but it is a waste in the sense that it is CPU mining which is far less efficient than mining with GPUS or ASICS.
There are proof of work algorithms that try to be ASIC-proof. And most visitors already have a CPU and GPU sitting idle. Something that used an extra 25% of your processors may not even be noticeable, and yet it could solve the fake news and clickbait problems.
Clickbait and fake news are not solely driven by advertising revenue so even if idle CPU and GPU had zero marginal cost crypto would not eliminate them. On top of that utilizing idle capacity is not free. The cost associated with crypto algorithms is real and must be evaluated in the context of what else could be done with the energy and compute resources. It’s not clear to me that crypto is the best use of our resources.
Is there a way to be ASIC-proof without being less efficient? I'm not 100% familiar with it, but my base level understanding was that you are adding more work (e.g. memory access) to nullify the raw compute advantage of ASICs.
Further, I'm not sure how it would solve clickbait. Surely clickbait => more clicks => more people running your miner (just as it currently leads to more ad. views)?
The thing is, finding a nonce that with given payload gives a hash ending with
predefined number of zero bits has only one purpose: so everybody is very slow
in computing it, but everybody is very fast in verifying. You can trade it for
any other difficult problem that's easy to verify (anything NP-complete will
do, assuming P != NP), you just need to find encoding that maps a payload into
a problem instance.
In other words, you could replace proof of work with finding the largest
clique in a graph, and try doing that in ASIC.