Just taking a stab at this, but NYPD cops may view the random search as fruitless. Little old women and babies are not terrorist bombers - searching them means nothing. Profiling is a tool that is not being used in NY - although it is used effectively in many other law enforcement capacities.
I may be wrong, but I know cops don't like to waste their time.
Your right, they also don't being penalized for doing their jobs and they don't like getting blamed for political pandering.
NYC also penalizes its cops for not meeting "performance goals" (i.e. ticket quotas).