Why must the Europeans be like this? Why do they insist on fucking with a free and open internet instead of addressing the apparently unmet demand that is fueling a black market?
If the US wants some content gone from the internet, they (usually) have enough might to make that happen.
Most major tech companies are registered in the US, and can be ordered by a US court to stop providing services to pirates. This notably includes most major DNS registrars, reputable ad networks and major payment processors.
There's no point in blocking a website if you can just boot it off Visa, or force it to show penis enlargement / shady gambling ads or malware popups to survive.
Even if a website miraculously has no US links to exploit, there are extradition treaties, good relations with foreign law enforcement, control over the financial system, or even international sanctions if the situation gets dire enough.
European countries are far less powerful here, especially when they act alone (as they usually do in these matters) instead of doing it under the auspices of the EU. Site blocking is often the only remedy they have.
The US has an opposite problem with scam calls. Because there are so many English speakers in India, and Indian law enforcement largely doesn't care about scammers as long as they scam foreigners, there's little the US can do about the issue. European countries whose first language is not English have it much easier, as there's often no third-world country that speaks the same language and where the scammers could be recruited from.