What about websites providing CSAM, hosting livestreams of animals being tortured for payment, selling drugs, etc…

Blocking a website is the only way for a country to stop these kind of illegal activists, short of shutting down the physical servers.

That statement doesn’t really make sense. Especially in this case, the website is a business and a store. A government definitely has the right to take legal action against a physical store operating within it’s jurisdiction, so why would the same not hold true for an electronic one?