The cop doesn’t HAVE to “run your plate”. In most cop cars, there’s a camera that scans every license plate it sees and runs a make on them.
Depends on the city. In 2006 I was at my brother’s house in Ventura Calif and he’d listen to police radio feeds on the internet.
They were still using crappy radio tech and calling into dispatch to run plates.
Unions.
The cop knows who’s car it is, and if everything is current before he pulls you over. The plate scanning cameras and software have become a constant super fast computerized monitor of the public.