All this is true, but also somewhat irrelevant. In reality the amount of actual hash work is completely negligible.

For usability reasons Anubus only requires that you to go trough a the proof of work flow only once in a given period. (I think the default is once per week.) That's just very little work.

Detecting you need to occasionally send a request trough a headless browser far more of a hassle than the PoW. If you prefer LLMs rather than normal internet search, it'll probably consume far more compute as well.