By having a team of people whose only job is to investigate the police, they look bad if they don't uncover issues like this.
I suspect the mistake in the US is that all the people who could punish the police are 'too busy' with other things. Make a dedicated team who has nothing else to do, and suddenly they'll be snooping around like journalists looking for dirt so they can make a conviction and get a promotion.
FBI doesn't want to investigate LAPD. They need LAPD, down the line, when there's some case for which they'll need cooperation.
What's needed is a Federal policing agency tasked with investigating and prosecuting police misconduct. That's the whole remit; police misconduct is their alcohol, tobacco, and firearms.
I suspect the mistake in the US is that all the people who could punish the police are 'too busy' with other things. Make a dedicated team who has nothing else to do, and suddenly they'll be snooping around like journalists looking for dirt so they can make a conviction and get a promotion.