I have a problem with most cop show protagonists. These cops are supposed to be liked by everyone, so everyone can root for them, and that's why they end up as empty shells. IRL, everything you do and like as a character, also says something about the things you don't do, and don't like. That's why these people never enjoy or do anything out of the ordinary, because it would scare part of the audience away from them. The one thing we know about John Luther, for example, is that he likes David Bowie. David Bowie is one of the biggest superstars ever, which is why when someone likes him, it really tells us next to nothing about them.
Of course, most fictional characters are written like this, but it becomes a problem with cops in particular, because these soulless, empty shells, robts almost, who cannot be defined by or criticized for anything, invariably end up judging and criticizing everything and everyone around them. They don't care about anything, they don't identify with anything except their work, and they regularly disrespect the interests, fashions, philosophies, etc. of all the bad guys, who might be assholes, but seem like real people.
I read an interview with the creator of the show Luther (I use this show as an example, and can still somewhat enjoy it), where he said that the character was designed as someone who buys a bulk of the same clothes, because he is so caught up in his work, he can't be bothered to pick a new outfit every day. - And he called this an IDEA he had for what Luther would be like. Dude, that's not an idea. It's a stereotype floating around in the ether, and you didn't write it so much as you just perpetuated it.