Scrapers, on the other hand, keep throwing out their session cookies (because you could easily limit their access by using cookies if they didn't). They will need to run the PoW workload every page load.
If you're visiting loads of different websites, that does suck, but most people won't be affected all that much in practice.
There are alternatives, of course. Several attempts at standardising remote attestation have been done. Apple has included remote attestation into Safari years ago. Basically, Apple/Google/Cloudflare give each user a limited set of "tokens" after verifying that they're a real person on real hardware (using TPMs and whatnot), and you exchange those tokens for website visits. Every user gets a load of usable tokens, but bots quickly run out and get denied access. For this approach to work, that means locking out Linux users, people with secure boot disabled, and things like outdated or rooted phones, but in return you don't get PoW walls or Cloudflare CAPTCHAs.
In the end, LLM scrapers are why we can't have nice things. The web will only get worse now that these bots are on the loose.