If you make it more expensive to request a documents at scale, you make this type of crawling prohibitively expensive. On a small scale it really doesn't matter, but if you're casting an extremely wide net and re-fetching the same documents hundreds of times, yeah it really does matter. Even if you have a big VC budget.
You can do more underneath Anubis using the JWT as a sort of session token though, like rate limiting on a per proof-of-work basis, if a client using X token makes more than Y requests in a period of time, invalidate the token and force them to generate a new one. This would force them to either crawl slowly or use many times more resources to crawl your content.
Anubis helps combat this because even if the scrapers upgrade to running automated copies of full-featured web browsers that are capable of solving the challenges (which means it costs them a lot more to scrape than it currently does), their server costs would balloon even further because each time they load a page, it requires them to solve a new challenge. This means they use a ton of CPU and their throughput goes way down. Even if they solve a challenge, they can't share the cookie between bots because the IP address of the requestor is used as part of the challenge.
Saving and re-using the JWT cookie isn't that helpful, as you can effectively rate limit using the cookie as identity, so to reach the same request rates you see now they'd still need to solve hundreds or thousands of challenges per domain.
Regardless of how they solve the challenges, creating an incentive to be efficient is a victory in itself. GPUs aren't cheap either, especially not if you're renting them via a browser farm.