I'll offer a different perspective on Looker.
First off, I wouldn't say he's a braggart at all. Most times he brings up being a member of the International Police, it seems like he's saying it naturally. Like how an FBI agent would say *Insert Name*, Federal Bureau of Investigation when bringing someone in.
I also wouldn't say he does nothing. He's actively investigating Galactic when he helps you get into their headquarters. Not to mention he personally arrests and brings in Charon in the Platinum post game using his Croagunk.
Looker also brings a different perspective to the series: the people who don't train Pokémon. He's only seen using a Pokémon once, as mentioned above, because his job simply doesn't require them. This, to me, isn't padding. It's world building. I like when there's lots of stuff to do in the main quest. I can't fathom how some people just speed through the story just to get to the post game stuff. Pokemon should be an experience, IMO.
That and XY gave Looker a lot more depth as well. It's heavily implied he's struggling to cope with the fact that his Croagunk died on the job, and he blames himself. He's also struggling to keep food on the table or keep his office, and it gets worse when he becomes a surrogate father figure to Emma. And then he has to cope with leaving her behind because he has to leave Lumiose due to his police work, giving Emma control of the Kalos detective agency. Yeah, he's bumbling at times, but it's his character flaw. He realizes it, and it's implied he feels great guilt over it.
So yeah, those are my thoughts on Looker.