Either the writers have absolutely no experience of how the police is supposed to work or they think that real police departments have eccentric obsessives like Sarah who screw up all the time because of their inability to stay on task and not be distracted into a tunnel vision state that causes them to screw things up colossally.
She constantly goes off the reservation based on an emotional reaction to something that's happening. She has no consideration for her colleagues or the general public - her disdain of politicians is justified as these seem far more concerned with accruing and retaining power than giving a rat's ass about the best interests of their country (typical parasite hacks) - and she is downright abusive in the way she treats those in her private life. She is a kind of monster and she seems to justify her reckless selfishness because she's trying to catch a killer. So what if her extraordinarily poor decision making has caused more deaths than the original crime?
I hope that no actual police department would ever allow such a massive liability on legs to be a meter maid ( she'd probably get kids killed if she was a crossing guard - distracted by something and letting cars plow into schoolchildren going to a playground) let alone an armed homicide detective.
Still the show is compelling and entertaining- despite the fact that I just want to slap her (and the nitwits who keep her on the job) every ten minutes.