Running a plate without probable cause is unjustified in my opinion.
That may be, but it is legal. Cops can now do it instantly from inside their car on a computer without calling it in. If a cop is behind you at a traffic light you can be sure they ran your plate.
That is the only reason to even require license plates, so cops can check them, and they do that constantly.
What would be probable cause?
Steal a car. . .no worries after that, just drive safe and you will never be caught. Ever. Unless you are involved in an accident or the original owner (victim) sees his stolen car.