Comment by chrismorgan

Proof of work is bad rate limiting. The power asymmetry is too immense. Worst-case example is SHA-256, where an attacker with dedicated hardware is millions of times as efficient as common users. Even with a less boneheadedly foolish POW scheme (quite incidentally, every single web POW scheme that I know of started with SHA-256, and almost all still use it), the ratio is easily in the hundreds or thousands, too great an imbalance to bridge. (That is: if you want to require an attacker to burn one second of computation time, some cheap smartphone user will now be stuck for five minutes. If you reduce the difficulty so that user is only stopped for five seconds, your attacker is now burning less than 20ms.)

Most web proof-of-work stuff has worked because it breaks the normal flow and the typical scraper is supremely dumb, not because of the proof of work, which has largely been a total red herring.