Your typical end user doesn't switch IPs that often, so it's fine to Anubis them again when they do. A scraper, on the other hand, has a tradeoff to make between rotating ips often (requiring a challenge on every request) or keeping only a few IPs (making cross-request identification much more valuable and reliable).
They meant you can’t PoW every page transition.
If clicking every link on your website throws you back to another Anubis page for 2-3 seconds, users will bounce.
That’s why Anubis does an up front challenge and then you’re good for a while. It’s a really low cost for the scrapers.
We can all argue based on how we envision "ideal" scraper networks being run and whether the web-PoW concept would stand up to that. However, what matters at present is that anubis helps many sites cope with misbehaving bot scrapers written by the script kiddies you mention, who don't care if the internet burns as long as they finish their scrape 1 hour faster. If anubis motivates them to devote a few brain cells to make their scrapers smarter, they may also fix the scrapers to not take down the sites they're scraping.