There already are nuanced exceptions. Technically, recording someone having a conversation on a phone can violate wire tap laws, even if you didn't interfere with the device. You can record police, but you're required to be back a certain distance (8' I think). Many states also allow private recording, but only if you reasonably believe a crime of violence might be committed. Etc

Ostensibly, the officer is open to a US 42 1983 color of law violation since there are court decisions affirming the right to record police in public.