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Haven't watched a single episode of the Ashnime since the start of Best Wishes but if here's my dumbass headcanon.
When a Pokemon is caught in a Poke Ball, it's traced back to the Original Trainer. When you trade, there's a log of that happening. Thus, any region's League can track you down if you're suspected of overhunting or funding an illegal fur trade. Stuff like that. Pokemon are also often seen coming out of their Poke Balls, which means that catching them standardly doesn't actually keep them locked inside.
That's why poachers in the Pokemon world often use alternative methods to Poke Balls. You can't track a simple cage and you can't just break out of being petrified. Illegal practices want to minimalize any sort of paper trail, a trail that Poke Balls leave.
