It's not explicit propaganda. It is a consequence of the setting, not so much an intentional goal of the series. I doubt anybody in the writer's room was like "How do we make cops likable to trick people into liking cops?" More like "How do we make cops likable because they aren't in real life?"
It paints them in a goofy, fun light and that can in turn make people subconsciously think of cops in a more positive way than they might not have.
I don't think it goes in heavy as actual copaganda like Blue Bloods, CSI, or other police procedurals but it has the shades of it.
It doesn't try to paint cops as being perfect, though. It shows how fucked up the system is to minorities and favors mediocrity and corruption within their ranks.
I just started watching Brooklyn 99 like...last month...and I love it a lot. I don't think it should disappear from television. In fact, it should go in hard as a commentary on current events. Or, like it has been suggested on Twitter lately, just have the new season with everybody working at the US Postal Service as investigators. No comments on why they are suddenly working at the post office (maybe a vague reference to them all quitting/getting fired from the force because they all went and marched) Same background characters, even recurring characters appear and are also suddenly working for the USPS.
