The only context I know them in is car chases/suspect spotlighting. If that's the primary use case, I imagine quadcopters eventually take that role for a lot less money.
At the same time, the FAA drone rules website does lead you to "Are you a Government agency (Federal, State, Tribal, and Territorial law), law enforcement, or a public safety entity?" and the rules LAPD would follow to operate a large drone are not the same as a random enthusiast would follow to operate a small drone. If the hypothetical drone is over 55 lbs, they might be operating just under the heading "Public Aircraft Operations—Manned and Unmanned".
https://www.faa.gov/regulations_policies/advisory_circulars/...
And even if that weren't true, law enforcement is a government operation and it's very plausible to see them get permitted to do things an average corporation or individual isn't. For example, extra requirements for flying near airports that require specific capabilities and sensors in the drone and a special pilot license.