No, Cloudflare should worry about what sites they host and enable. How Google ranks the sites that Cloudflare hosts is a secondary issue, and is outside of Cloudflare's control.
So every time anyone wants to report a site that is offering "Flash Updater" Trojans, someone should file a lawsuit?
Every time a scammer puts up a web site trying to sell counterfeit goods, the company which sells the real goods should file a lawsuit? One for each scammy web site, perhaps? Because Cloudflare shouldn't be expected to do anything at all, until they're compelled to do so by a court?
lol I don't think you understand how the legal system works. you don't file a lawsuit and go as a private unless you also are trying to recover claims, you report cybercrime to your local authority and let them pursue the criminal
You've clearly never reported cybercrime to the authorities if you think this would work. Or you have, and you think that only large businesses which can claim losses of $10,000 or more should be protected, and everyone else is SOL.