One problem with that is, how does the average person know whether a "Middle Eastern-looking person" is born in Syria or Schenectady? The three medical students who were arrested and detained for 17 hours after allegedly joking about 9/11 and discussing plans to carry out a terrorist attack were all US citizens - 2 naturalised, 1 born in the USA. Annie Jacobsen had no way of knowing whether the "terrorists" she still thinks she encountered on a flight to LA were foreign-born or US citizens.

The problem with eroding civil rights to combat terrorism is that terrorism is a response to the erosion of civil rights. As long as people feel that they have a legitimate way to make their grievances heard, they generally don't resort to terrorism. Terrorists generally are people who feel they are powerless to change the status quo in any other way.
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"The mind is not a vessel to be filled but a fire to be kindled."
-Plutarch