A reason why websites are so hard to take down is that they're so easy to set up. For example, the video streaming link hosting website primewire.org/ag/com was letmewatchthis.se/com/org/de and they all just reroute traffic. The point is that they are exactly the same website. As long as the Internet is around they can keep taking them down, but they'll just start again under a different name, and word eventually gets around via reddit/4CHAN, word of mouth and the cycle starts all over again. But recently I think link sharing websites are not illegal but Google can't put them on the top of their search results or something.
What's even better are the websites that they host their streams on are constantly changing names since they keep getting taken down, or throttled but the templates the websites use are exactly the same: the type of embedded video players, the font, format, etc. The only thing they change is the color and the name.
But yes banning a domain name is possible, or ICE can take it down but that only applies to American websites.
It's impossible for websites to be taken down but it is possible to limit their exposure and that is to have an American version of the great firewall, but that'll never happen, hopefully...