Simple incentives seem to explain that one without needing much of a conspiracy:
If you're buddy-buddy with the cops, they'll help promote you, talk to you about cool cases they worked, etc.. If you're instead critical of the cops, they're going to try and undermine you instead.
This means that doing a cop show that's anti-cop would be like doing a medical show without ever being able to consult a doctor. You can do it, but you're going to have to put a lot more work into research to get the same sense of verisimilitude.
You know how people who don't work in government don't realize Parks and Rec is a documentary?
And people who don't work in a white collar office don't realize The Office is also a documentary?
Well Brooklyn Nine-Nine is a documentary too.
The primary artistic liberty these shows take is to take a decade's worth of shenanigans, compress it into one season and cut out all the drudgery in-between. Basically all the stupid "that would never happen" crap happens but spread out over 100x as long and 10x as many people.
If you're buddy-buddy with the cops, they'll help promote you, talk to you about cool cases they worked, etc.. If you're instead critical of the cops, they're going to try and undermine you instead.
This means that doing a cop show that's anti-cop would be like doing a medical show without ever being able to consult a doctor. You can do it, but you're going to have to put a lot more work into research to get the same sense of verisimilitude.