Back in the stone age, I was leaving law enforcement in California about the time Paul was starting, I don't recall stopping anybody for a missing front plate. If my gut and my training told me that I needed to stop a vehicle, there was often probable cause to do so. On several occasions letting it be obvious that I was following somebody would trigger an episode of stupid driving and a car stop would ensue.
Robert's comment on traffic cops working just that is accurate. Beat officers on patrol were expected to respond to calls, be highly visible, look for trouble and conduct traffic stops for a variety of reasons, but always with probable cause.
Most common mechanical probable cause for stopping a car = burned out license plate light. Back then, they seemed to burn out a good deal. I routinely check mine on all my cars.