Actually, maybe they could - LAPD has had so many suits and consent decrees go against them, and a pretty rocky history, they aren't really the model of progessive, professional law enforcement, if they ever were.. What they do have is a great PR machine, but even that hasn't been doing so hot. They don't train there cops any better or worse than most big agencies, where the primary job of the Academy is to manufacture clones at high cost-efficiency.
Certain agencies like the FBI, LAPD and CHP get a lot of hype, because they've been hyped a lot. J. Edgar Hoover actively sought out Hollywood for the '60s program on the FBI and required his agents to provide whatever assistance was needed, but only when he was given the ability to approve every script and episode. And this was when he was playing lingerie model with Clyde Tolson and directing the agency to do patently illegal things to get and maintain political clout. Even after the rigime change the Bureau was rife with problems, little things like agents who were commie spys and a crime lab with zero internal auditing.
And if you don't believe me, ask somebody from LAPD, or the FBI.