It's legally much simpler to do so, and leave your offices in the cheap EU. US Inc can employ your offices and at the same time have no people working in the US.
US is saved by ruthless capitalism. When I see what politicians from my country voted on I'm realizing that journalists, political science majors, historians, spanish/english/lang language teachers, philosophers, artists and bunch of other social scientists know much about nothing - maybe it says something about our national universities, maybe about these science areas as a whole, who knows. But for some reason they think they are capable of having a career in politics, and it works.