90% of what most cops (but not all) will deal with when it comes to use of force is the non-violent but non-compliant individual.
A good example would be a non-aggressive intoxicated guy who none-the-less refuses to get out of traffic. A perfect situation for a cop to walk out and slap on some kind of "come along" AIKIDO wrist technique and walk the guy out of the street to the waiting patrol car.
Sometimes things escalate and the officer finds himself dealing with a subject who decides to fight back. Maybe shoves the cop or something, but has no weapon and is making no attempt to get the cops weapons. A hard JUDO takedown is in order, followed by a blast of OC Spray to the face.
Sometimes things get really nasty and the bad guy whips out a knife or firearm. The officer escalates his response appropriately and draws his firearm.
Cops have to be constantly concerned about their own duty belt (commonly called the "bat belt") which has a baton, pepper spray, taser, and a firearm among other dasteredly things that the bad guy can get ahold of.
BJJ is good, but a cop pulling guard would be downright stupid because of the bat belt problem, among other things.
Ever seen the video footage of the cop who ends up trying a kimura against the guy in his guard and the guy gets the cops duty weapon? He actually tried the kimura on the same side he was carrying his pistol, so that the bad guys hand was right on the firearm itself. Stupid.