I want two things in relation to cops.
1) I want to be able to be the cop, and chase my friends. Go through Police Acadamy training, start off assisting the AI, then after getting certain achievements, becoming the seargant in charge of the pursuits, the one who can call for backup, roadblocks, spike strips, helicopter, shoot tyres, etc.
2) Cruise/race with friends, then accidentally run into cops, be it AI or other players, where the cops chase us as a group, then as we split up, they have to choose who they will target. Your friends, sensing that they've evaded can then come back to help crash out the cops for you, or crash you out to try and help the cops. This shouldn't have to be a specific cops'n'robbers game mode, but just built in. Options can be made available so that players can opt out of Cop mode, where their server won't have any user police, only AI.
Instead of just always seeing KENNEK43 online, I'd see a trail of police cars behind him as well :)