The American system's "blindness" cuts off the most important weapon in the war against terrorism: Human capability, judgment and perception. Now that the United States faces a higher threat, it cannot afford to neglect those tools.
Using sociological data as well as constantly updated intelligence information, trained security personnel know who is most likely to be perpetuating an attack, as well as how to identify suspicious individuals through behavior. (Again, it is important to note that ethnicity is only one factor among many used to identify potential terrorists.) Removing intelligence and statistical probability as tools would render this model far less effective.
Random searches of grandmothers and congressmen may make Americans feel virtuous, but they don't keep Americans safe. The attacks of 9/11 and the attacks on public transport in Madrid and London sadly demonstrate that Americans cannot afford feeling virtuous at the cost of human life.