This is exactly why I struggled with the show. Maybe it's the Japanese way of storytelling or maybe it's my own inability to follow the subtlety, but I didn't like how the story was revealed to the viewer. In the very first episode they show the system is flawed (someone in shock or having a trauma response is ordered to be executed) but then the rest of the show just continues on anyway. So in the very first episode we're shown that the crime coefficient can't be trusted and yet we spend the rest of the show continuing to trust the crime coefficient.

I guess I didn't get the sense that people were trying to fix a broken system; I got the sense that the main character had some initial doubts but didn't do anything about them until the end of the season. In most episodes, the main cast are doing everything they can within that system and continuing to trust the system. It's not like they were loose cannons solving crimes their own way, they were very much still following the system. Well, I guess the latent criminals were sometimes loose cannons but I though that was treated more as characterizations of them being "latent criminals" rather than a critique of the broken system.

Again, this might just be the Japanese way of going about it. If this were an American show, they'd probably start with a "true believer" who gradually learns to distrust more and more of the system as they get more of an inside view into how it works. Maybe the Japanese way is to immediately learn how things are broken but be forced to continue acting like nothing is wrong.

Anyway, I like your interpretation of the show and I agree it's probably what the showrunners were going for. It's just not what I got while watching the show. I felt like most episodes showed the system working as intended, not a broken system.

Now that you've got me thinking about it, I'd compare it to hard-boiled detective novels. In hard-boiled detective novels, the police force is also a broken system. They're incompetent and can't be trusted. As you said, the system is broke and will always be broke. So the hard-boiled detective works outside the bounds of the police force to get things done. I'd argue the hard-boiled detective isn't trying to fix anything, but I wonder if that's the difference between the American approach and the Japanese approach. One attempts to work within the system while the other will ignore the system to do it their own way.

Sorry for this long rambling comment but your comment got me thinking and I just kept running with it...