Perhaps rather than random searches, they would be better off investing the money in some kind of "metal/bomb detector device to install at the subway entrances?
I have lived in NYC and took the subway every single day to work and back. You would not BELIEVE the things people bring/have on the train with them....there were many times that I thought to myself that I was the only sane person in the car.....
Twice, in the six months I lived there, innocent people were thrown in front of the train and died...I used to hold onto the pole while I was waiting like my life depended on it...and if just might have....

We have been much too complacent in this country, thinking, it will never happen to us...and then it did....and how quickly we have forgotten.............
If you have nothing to hide, what is the problem? Big deal if they see your tampons or your birth control or your self-help book....or whatever it is that is private to you? If you are not trying to kill innocent people, they don't care and you shouldn't either!!!