Under what law? It's interesting because these are sites that host content for the purpose of providing it to anonymous network users. ebay won a case against a scraper back in 2000 by claiming that the server load was harming them, but that reasoning was later overturned because it's difficult to say that server load is actual harm. ebay was in the same condition before and after a scrape.

Maybe some civil lawsuit about terms of service? You'd have to prove that the scraper agreed to the terms of service. Perhaps in the future all CAPTCHAs come with a TOS click-through agreement? Or perhaps every free site will have a login wall?