One gameplay abstraction the pokemon franchise makes that I've always found interesting is the way traded pokemon only obey you if you have enough badges. While it obviously exists to avoid people trading in overpowered pokemon and stomping the game, the idea that a pokemon would know or care how many badges their trainer has always struck me as odd, and with the Arceus game instead attributing obedience to a player's rank as a researcher, I want to make an argument that it is not literally about the badges, but about experience.
With every badge, the player character becomes more experienced. They, in-universe, exude more confidence, and appear more formidable to others. Rather than an arbitrary badge or rank, this is what the pokemon respect, they see the confidence the trainer issues the commands with, confidence gained from experience, and that's what makes them follow the orders. By the time you've gained your last badge in a pokemon game, you've usually taken down a crime group and stared down a god. The trainer with 8 badges is simply a different beast than the one that set off from their starting town.
That's just how I like to think of it anyway.
in the manga the badges were made of special stones that exerted will over pokemon