One or more of the background sounds in Underground 2 include siren sounds, even though you never see a police car. The sirens could be from a non cop type vehicle though. Most Wanted expanded the list of background sounds, and the list of background sounds heard in Most Wanted make up almost all, if not all, the background sounds heard in Carbon and Undercover (Undercover has a unique thunder sound, but it never rains in Undercover).
Back to the Bayview police time trial records, there's no reason they could not travel from west coast USA (Bayview) to east coast (Rockport) for these competitions.
Then I go back to my initial idea. Underground 2 is the 1st free roam NFS and they coudn't find a way to introduce cops too. Evn in a free roam race the AIs behave like they have been lost sometimes. They don't have a good definition in following you so you can imagine why there are no cops. Better than s faliour... sonething missing.