Not a police officer myself, but based on what I've read on the subject, you seem to be describing
duty lights more than
tactical lights.
The way I see it, the duty light is used for all the routine work that's probably >95% of uses. Traffic stops, accident investigations, surveying a scene, terse-but-not-violent interactions with suspects, vehicle searches, investigation, etc. Needs to run for hours at a time, but not necessarily at high intensity. Needs to be handy, but need not be an ergonomic wonder.
The tactical light could do a lot of the duty light functions, but that's not how it seems to be popularly imagined.
Instead it's seen as something drawn for the purpose of a gunfight, SWAT deployment, searching for an armed suspect, or any high speed low drag imagery that can be made to stick. High intensity, short runtime, compatibility with picatinny rail or 1" mounting rings, momentary operation as primary mode, tailswitch, and expensive to operate seem to be their hallmarks.
There is surely a place for both in police work, but I suspect the latter's is a bit over-emphasized.