With a monolithic culture, a purely random process makes sense... Could you please direct me to that imaginary monolithic culture? I want to move there and F*ck it all up...
Imagine wasting 70 percent of your time searching grandmothers, children, and the handicapped instead of searching the more likely demographic. It's pure idiocy to think profiling is a bad thing. If you are profiling to harass then yes it is bad but if you are profiling because the profiled group is doing all of the bad things then profiling is not bad. Only an idiot can't see such an obvious truth...
If you have a building with four entrances, and you have twelve guards to cover them, do you put three at each entrance, covering each as best you can, or do you put nine on one entrance you think is most likely to see an attacker, and only one on each of the other three?
If you're an idiot, you do the latter. If you're not an idiot, you realize the former yields maximum security, because as soon as you put all your guards on one entrance, it becomes far easier for an attacker to get in, they just use one of the other three.
If you can understand that, you should be able to comprehend why searching any particular demographic more (and thus, by diverting resources, means you search others less) makes you less secure, not more. As soon as your move resources into an uneven distribution mode, you open up exploitable holes, and you're a moron if you think your enemy won't exploit that.
Your "obvious truth" is the kind of thing uneducated people who don't really understand the problem say. Answers always seem obvious when you don't understand the problem -- but you could actually try educating yourself before spouting off idiotic nonsense...