Private third parties are an inappropriate place to enforce the law. If you have a dispute with someone, you sue them, not their hosting provider. Then they have to pay you damages, the court will order them to stop, if they don't stop there are criminal penalties for contempt of court, etc. Why is the hosting provider even involved?
> a huge quarrel of lawyers
That's not... No, I'll allow it.
> Right now, for example, a phishing site is hosted via Cloudflare at "schwabs-wild dot com". Cloudflare replied to a complaint about it in less than a minute and a half to say:
> "We were unable to confirm phishing at the URL(s) provided."
Well yeah, because they're not law enforcement and they have no way to know if that site is a phishing site or a real or testing service by Charles Schwab or one of their subcontractors, or a honeypot or some law enforcement operation or the subject of an ongoing investigation the police don't want to spook etc. Meanwhile they get tons of fraudulent complaints from trolls and the competitors of their customers trying to take down their legitimate sites.
Stop expecting them to be a court. Go to a real court and get an injunction. Or report it to Charles Schwab or the police rather than Cloudflare so they can do it.