Live for Speed would be brilliant if it had police chase game-modes. The idea I had in mind was this:
You drive around the track as normal, only one player/team are in police cars which are LFS cars but with police skins (excluding F1 cars) and the other player/team are in normal LFS cars (excluding F1 cars) and the police either have to crash the other drivers or stop them in another way. Ie. Surround them in team-mode or hand-brake turn in front etc.