I’ve hosted content online for decades and never once talked to cloudflare.
And just a few hours later, I received a letter informing that the information about the website in question had been forwarded to the relevant authorities, as well as to the website’s hosting provider. To be honest, I didn’t read that second email until the next day (I was sleeping), and it seems the website's hosting provider acted quickly (or the site owners decided to cover their tracks), because when I went to that website to check how it is going, it was no longer active, no longer existed at all. It just was gone. That was about six months ago.
So... I won’t speak for others’ experiences, but in this particular case, they reacted quickly and quite effectively. Perhaps other people have had different experiences.