Man, I've heard that the poke-rpg is fucking busted as hell but that still sounds really fun. Bit envious.
I haven't watched the animu in years, but from what I remember, they were good at setting up the adventure of the day. Like there was one that took place in the safari zone where they encountered a young boy who'd been raised by kanghaskan, or one where they came across a haunted house that was infested with ghost pokemon, stuff like that. I think in the ghost one, one of the members of the party got their soul stolen by a ghost, and then the others traversed the house to get him back, right? That's a decent set-up for an adventure. No need to copy the cartoony feel, but the situations were ripe for exploration.
On a personal level, I think if I were DMing a pokerpg, I'd try to puzzle out in my head how the pokemon setting would actually work. Are there jails, mental institutions, or rehabilitation centers for misbehaving pokemon? What different modes of transportation could various pokemon provide? Are there political conflicts between nations that could arise because of pokemon (banned wailord hunting? using pokemon as chemical weapons in warfare? Maybe too grimdark for a light-hearted rpg, depends on tone). The weather trio could have a tiff that wreaks havoc on the world's weather, upsetting climate-reliant pokemon in its wake.
It's a rich world, man, go nuts.
And what about legendaries? Besides the typical "team whatever wants to misuse a legendary," they're extremely powerful beings with their own agendas. Celebi can drag you through time if it needs to.