Re: Missing the point
"If an author writes a book that plagiarized, violated the copyright, of another book, and is published[, o]k, who violated the copyright? The writer who wrote the book, or the publisher who distributes the work for him?"
Good analogy. Let's use that. They are both liable, and for a very specific reason. Both of them know what is in that book. The publisher knows because the publisher reviewed it. The publisher employs editors for that purpose, because they're restrictive about what they publish. They therefore know a crime is being committed.
Here are some people who are not liable: the paper mill, the printer, the bookbinder, the delivery driver, the book storage warehouse, and the book shop. Here are some people who might or might not be liable: the literary agent, the illustrator, the copy editor (if there is a separate editor who looks for typos and grammatical problems), and the contents of the acknowledgements section.
The thing which determines whether those listed under "might be liable" are or not is whether they know the crime is taking place. For the same reason, the people listed under "not liable" are there because they don't know about the crime. And that is the situation here. CloudFlare is useful to criminals, but it didn't design itself in that way, it is useful to law-abiding people as well, and it doesn't know which is which. In addition, they comply with the laws that currently exist which restrict what services they can provide.
If you want service providers to individually monitor what the customer is doing in order to more quickly enforce the law, you can pass a law to that effect. Such laws have been proposed before, but most countries don't have one. In my opinion, that's a very bad idea, but if enough people disagree, you can do it anyway. Until you do, don't expect companies to voluntarily do so.