Kate (Emily Blunt) is beyond aggravating to watch
First of all, I like this movie, Del Toro is badass and Sicario is realistic.
For the first 15 minutes, i think Kate is okay, but contrary to what many believe, i don't think they picked her because she was dumb. At the Beginning Josh Brolin hears she has worked for the FBI as a door kicker for years and thats all she's done. he says "I like her already" They were picking an FBI Agent so they could operate where they needed to, yes, but they also wanted someone who wants to see justice brought to the cartel members involved with the bomb earlier that day- who hated those responsible and had tactical experience.
Then all throughout the action she does stupid nonsense stuff; starts smoking again, freaks out when her team kills 8 of the worst people in the world (who were going to attack) points her glock at her savior, almost lets a corrupt cop bang her (then almost murder her) and in general tries to hinder her team mates. That is why they didn't make her a bigger part of the team/tell her anything. The CIA Josh Brolin and Alejandro were not corrupt, they did not take money, they simply did what they were supposed to well.
She also acts like everything must be done by the book, yet when she was almost killed by a corrupt cop she tries to screw, I bet that wouldn't be in her official statement of how they caught him.
Perhaps she was just simply the wrong choice for a badass woman type.