Several decades ago, when video cameras were a new item, some activist organizations bought a bunch and distributed them to some people in the hood so they could document police actions. The instructions were to keep their distance - filming from across the street was the preferred technique. Police were not amused, and tried mightily to suppress their actions - I recall seeing videos of cops trying to steal the cameras of other videographers - not pretty. I even recall a case where police saw someone filming them from inside their own house and began pounding on the door, demanding the tape.
IIRC, Chicago actually had a local ordinance for a time which prohibited photographing cops - I don't believe it stood up to a court challenge.
With camera enabled smartphones today being nearly ubiquitous, it's nearly impossible to stop photography in populated areas. Best they can do is try to keep people back - I know if I were photographing cops in action, I would definitely keep my distance since I wouldn't want to become part of the story myself.