Consider:
An adaptive password hash like bcrypt or Argon2 uses a work function to apply asymmetric costs to adversaries (attackers who don't know the real password). Both users and attackers have to apply the work function, but the user gets ~constant value for it (they know the password, so to a first approx. they only have to call it once). Attackers have to iterate the function, potentially indefinitely, in the limit obtaining 0 reward for infinite cost.
A blockchain cryptocurrency uses a work function principally as a synchronization mechanism. The work function itself doesn't have a meaningfully separate adversary. Everyone obtains the same value (the expected value of attempting to solve the next round of the block commitment puzzle) for each application of the work function. And note in this scenario most of the value returned from the work function goes to a small, centralized group of highly-capitalized specialists.
A proof-of-work-based antiabuse system wants to function the way a password hash functions. You want to define an adversary and then find a way to incur asymmetric costs on them, so that the adversary gets minimal value compared to legitimate users.
And this is in fact how proof-of-work-based antispam systems function: the value of sending a single spam message is so low that the EV of applying the work function is negative.
But here we're talking about a system where legitimate users (human browsers) and scrapers get the same value for every application of the work function. The cost:value ratio is unchanged; it's just that everything is more expensive for everybody. You're getting the worst of both worlds: user-visible costs and a system that favors large centralized well-capitalized clients.
There are antiabuse systems that do incur asymmetric costs on automated users. Youtube had (has?) one. Rather than simply attaching a constant extra cost for every request, it instead delivered a VM (through JS) to browsers, and programs for that VM. The VM and its programs were deliberately hard to reverse, and changed regularly. Part of their purpose was to verify, through a bunch of fussy side channels, that they were actually running on real browsers. Every time Youtube changed the VM, the bots had to do large amounts of new reversing work to keep up, but normal users didn't.
This is also how the Blu-Ray BD+ system worked.
The term of art for these systems is "content protection", which is what I think Anubis actually wants to be, but really isn't (yet?).
The problem with "this is good because none of the scrapers even bother to do this POW yet" is that you don't need an annoying POW to get that value! You could just write a mildly complicated Javascript function, or do an automated captcha.
