>>45958802I actually don't think that Champions are at all involved in government.
If you look at the world of the games, the Pokemon League in most games except for Alola and Galar is really more of a self-contained, glorified country club sort of deal. Gym Leaders, Elite Four members, and Champions are regarded as powerful trainers and may also be seen as important figures in the community and/or celebrities depending on their jobs outside of their respective Leagues. But at the end of they day, they aren't involved in politics and law. Champions and Gym Leaders may choose or be called upon to help law enforcement out where they can because they're powerful trainers, but I don't think that's in their job description.
Diantha is a perfect example of this. She's the Champion of Kalos but has nothing to do with the International Police and has no ties even to the Lumiose Police Station. Throughout Kalos, she's really regarded as a famous actress who also somehow managed to find the time to become the champion of her region's Pokemon League. The only reason that she gets involved in Team Flare matters is because she has a personal relationship with Lysandre.
Another example comes from the fact that police officers are often NPC trainer classes that likely don't take orders from Gym Leaders or the Champion and can apprehend them for criminal activity like Giovanni. Nanu from Alola also gives a glimpse that Pokemon Leagues are separate from law enforcement because of all of the island Kahunas, Nanu is the only one to actively become a police officer. This would be a redundant action if essentially being a Gym Leader already granted him that authority.
