The very first cop show, Dragnet, was explicitly a PR move to rehab the image of the police in the public's imagination. Every cop show since has been propaganda. Even shows where the police are not necessarily the "good guys", like The Shield or even Chicago PD, normalizes police brutality and the flaunting of basic constitutional laws because those dastardly bad guys have to be stopped at all costs.

I enjoy some of these shows myself but it is sometimes crazy how blatant they are about it.

It's definitely. Notice how after the 1994 Crime Bill was put into effect you had a large wave of shows and movies that increasingly depicted police as tools of the state rather than as protectors of the public. The fact that police-centered media exploded in ever larger shockwaves after that, the Atlanta Centennial Olympic Park Bombing, 9/11, and the deaths of Trayvon Martin and George Floyd was no coincidence. Law & Order, NYPD Blue, NCIS, Chicago PD, and Blue Bloods each correspond to each of those periods. The shows and movies are designed to make the abusive and destructive actions of the police look gallant. The police themselves actually advocate on many of them in order to sensationalize depictions or manipulate points of view so that they can then take them and use them as emotional appeals when the public criticizes policing.

The name "Law & Order" is a blatant example of this, as it's a phrase used by Richard Nixon during his campaign in 1968, and was widely repeated when he created justifications for starting the War On Drugs in 1970. This same phrase was later used by Reagan and H.W. Bush when they planted their positions of wanting to wield state violence against countercultures that arose. The '90s was full of change as Gen-X started to become adults and formed their own powerful countercultures, and the title of the show was an emotional appeal to conservative older people who hated that change and wanted the state to shape society instead of the other way around.

It’s the entire reason some shows and movies exist. The Pentagon, CIA and other agencies routinely and openly assist hundreds of films and TV shows with equipment, locations and expertise in exchange for script changes that protect U.S. military and intelligence reputations.