Most airport screening is for smuggling, not terrorism. Countries automate the process to stop corruption, so that airport security can't shake down passengers for money. None of this applies to stopping terrorism in the United States.
The reason randomized screening stops smugglers is that it changes the risk/reward ratio. It's not worth smuggling a $1-million of diamonds through the airport given a 5% chance of them getting confiscated. It's not worth smuggling $100 of cocaine through the airport if there is a 5% chance of going to jail. It stops professional smugglers, those who do it repeatedly, because it means they'll eventually get caught.
This math works in the opposite manner for terrorists. Their goal is to die in fiery crash. A 5% chance of getting caught means a 5% chance of living. For some weapons, like guns, they aren't likely to even go to jail, as a thousand people a year accidentally bring weapons on the plane without severe consequences. For other weapons, like C4 packed in a Koran, the press generated from the attempted terrorist attack will be nearly as good as a successful attack. In any case, if their first minion gets stopped in a randomized search, the terrorist organization will just send a second one.
Thus, in the words of Bruce Schneier, randomized screening is just security theater. It has little deterrent effect on terrorists.
Schneier says that the automation is good because it's free from bias or profiling. But that's not "security" speaking but "left-wing populism". Bias and profiling is good from a security perspective. Focusing your attention on mid-eastern males is more secure. Punishing white grandmothers because you feel guilty about the unfairness of profiling is just stupid.
Certainly, profiling is bad for society as a whole. It's bad for crime, for example. If young black men believe they are going to jail anyway, fairly or unfairly, regardless of what they do, they are more likely to commit crime (as John Adams once pointed out). The more we treat an ethnic minority differently, the less they will assimilate, and the more likely they are their children will want to rebel. That government does profiling in some cases sanctions intolerable bigotry in others. Whatever your politics, there are good reasons to avoid profiling.
But just because profiling is bad in general doesn't detract from its value in the narrow case of "airport security". Automating selection certainly fixes the societal problem, but by destroying any usefulness selective screening has in stopping terrorists in the first place. Therefore, the correct solution is to get rid of selective screening altogether, not automate it to assuage your guilt.
Update: The ever awesome Sergey Bratus points to this NYTimes article that says, and I'm not making this up:
"If terrorists learn that elderly white women from Iowa are exempt from screening, that’s exactly whom they will recruit."I think we have such a fear of being called "bigots" that we'll pretend to believe the plausibility of this statement (h/t Marsh Ray). We should just replace profiling with other security techniques, or simply live with the increased risk, not discard logic because we dislike the practice.
Update: Bruce Schneier responds, characterizing my argument as "profiling makes sense". No, my argument is "random selection doesn't make sense" -- regardless of the efficacy of profiling. I only mention profiling because I believe political correctness encourages people to thing wrongly about random selection. The correct policy is to stop the invasive screening, either from profiling or random selection.