This is the country that banned Tiktok, inacted the DMCA. Apparently the US has blocked 1.2m websites since 2010. They sieze domains, sieze servers. They stop payment companies working for the sites.
There are plenty of states in the US that enacted age verification laws for porn sites. Every single one of the porn sites that are not hosted in the US just ignored the laws. I live in one of those states
If this was a federal law (and one that the government actually cared about enforcing), it would be a different matter entirely. Case in point, all the crypto services that make themselves unavailable to AMericans, even if they have no direct links to the traditional financial system, much less American banks.
Site blocking is the lazy solution favored by bureaucrats who don't understand technology and as an easy way out for their tech companies from having to adapt to what the people are demanding (and getting from the black market instead). If the streaming services refuse to offer what the people want, then the people will bypass them.
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.