Agreed. Here's one possible solution, no doubt flawed. Remove the safe harbor provision that allows companies to profit from pirated software they publish, even inadvertently, pirated content. Provide an avenue to financially penalize companies that run for-profit websites so that copyright owners have some recourse. 5k to 10k per instance, and allow some practical due process (as is now the case for DMCA take downs.
The solution is simple on one level. As with other criminal endeavors where you can't always get at the origin, REMOVE THE FINANCIAL INCENTIVES for piracy AND send the message that major companies Google (owning YouTube), ScribD, and so on who plaster and profit from ads on stolen content, MUST self-police or compensate owners.
The idea is not so much to actually fine companies but to say: We will no longer allow you to profit from theft that you enable. The principle has precedent that if you aid and abet breaking the law, you may be held just as liable as the people actually breaking the law.
If I know I can recoup my time and energy trying to enforce my copyrights, then I can do so. I guarantee you that within one week of having such a law in place, google (addressing its ownership of YouTube and Blogger, two of the worst stolen works dissemination spots) and other companies would hire hundreds of people to protect their interests, putting them on the right side of the law and on the same side as intellectual property creators.
Hundreds of thousands of pirated sites and content would disappear in a matter of weeks. In addition, address google's adsense program, which is used to profit from posting pirated content. Hold them responsible for transfering money to pirates via the ads displayed and supplied by google. The same for other ad companies, some of whom are even more lenient.
One doesn't have to "cut off" foreign sites from the entire Internet, but REMOVE their ability to make money through crime, and since most of the avenues to do so operate within the USA, make the accomplices accountable.