Brain Gain through wise immigration policy

I quote from the Brookings Institution website on "Brain Gain":

Many of America’s greatest artists, scientists, inventors, educators, and entrepreneurs have come from abroad. Rather than suffering from the “brain drain” of talented and educated individuals emigrating, the United States has benefited greatly over the years from the “brain gain” of immigration. These gifted immigrants have engineered advances in energy, information technology, international commerce, sports, arts, and culture. To stay competitive, the United States must institute more of an open-door policy to attract unique talents from other nations. Yet Americans resist such a policy despite their own immigrant histories and the substantial social, economic, intellectual, and cultural benefits of welcoming newcomers. Why?