Little things like this annoy me too, destroying the reality of the show!
Just like when they are driving a new model Suburban or truck in a show, but blow up a 10 yr old version in a scene a few seconds later!
I'll bet that the producers/directors/etc would rather have a bogus FL front plate on the cars, rather than an empty hole or empty front license plate holder on the cars, since they are all likely CA cars that require the front plates.