No. The servers in the data center are rented to specific clients. If these clients commit crimes and the DC operator knows about it but chooses not to shut down the offenders, that's their business feature.
I'm considering the previous posters comment on how the users who post illegal materials should be responsible, not the platform. But yeah that makes sense. In this case it would be as if the city knew about the child pornography on the street but decided not to do anything about it.
Not really. More like the city rents out the light poles to companies who can staple messages to them. Some companies put up CP. The city then tries their best to not shut them down, and protects these companies because they pay rates that are way above market. I.e. the "not taking it down" is part of the deal.