"It pains me to say this, but I think that differentiating humans from bots on the web is a lost cause."
Ah, but this isn't doing that. All this is doing is raising friction. Taking web pages from 0.00000001 cents to load to 0.001 at scale is a huge shift for people who just want to slurp up the world, yet for most human users, the cost is lost in the noise.
All this really does is bring the costs into some sort of alignment. Right now it is too cheap to access web pages that may be expensive to generate. Maybe the page has a lot of nontrivial calculations to run. Maybe the server is just overwhelmed by the sheer size of the scraping swarm and the resulting asymmetry of a huge corporation on one side and a $5/month server on the other. A proof-of-work system doesn't change the server's costs much but now if you want to scrape the entire site you're going to have to pay. You may not have to pay the site owner, but you will have to pay.
If you want to prevent bots from accessing a page that it really wants to access, that's another problem. But, that really is a different problem. The problem this solves is people using small amounts of resources to wholesale scrape entire sites that take a lot of resources to provide, and if implemented at scale, would pretty much solve that problem.
It's not a perfect solution, but no such thing is on the table anyhow. "Raising friction" doesn't mean that bots can't get past it. But it will mean they're going to have to be much more selective about what they do. Even the biggest server farms need to think twice about suddenly dedicating hundreds of times more resources to just doing proof-of-work.
It's an interesting economic problem... the web's relationship to search engines has been fraying slowly but surely for decades now. Widespread deployment of this sort of technology is potentially a doom scenario for them, as well as AI. Is AI the harbinger of the scrapers extracting so much from the web that the web finally finds it economically efficient to strike back and try to normalize the relationship?