The US wouldn't have to do that, they can go after the financial side of the business. They could prosecute or make the lives of any persons involved with these companies very difficult financially. Imagine trying to do business in the US when no credit card processors, banks, or other financial institutions will touch you with a mile-long pole. Now imagine facing that not as a company, but as an individual; How comfortable of a life do you think you'd have as a person living in the US and being unable to access practically any financial institution? And even outside the US, how many companies with a US presence would kick you out to avoid Uncle Sam paying them a visit?

It's only partially a technical problem -- most of the issue lies in the rubber hose.