Fareed Zakaria's latest article in Newsweek details this problem. Perception matters. In fact, in most cases perception is reality. We do not need to be perceived as a closed state.
The visa process is so cumbersome that many foreigners have stopped trying. Business travel into the U.S. is down 10 percent.
"...Arab leaders landed at John F. Kennedy airport. The first group of participants, mostly CEOs of large companies, were pulled out of the regular immigration lines and made to stand for two to five hours while Department of Homeland Security officials grilled them as to why they were coming to America, whether they had any experience using weapons, what they thought of the Iraq war and other such questions. Half a day into their trip, before they had even left the airport, they were angry and humiliated. So much for improving America's image in the Arab world...."