I would love to see them shifting some of the focus away from the inaugural "I am to be a Pokémon Champion"-theme. Any excuse for a story would work, it would probably be a step in the right direction as long as they keep it light-hearted. Searching for your older brother or sister who left for adventure some two years ago, whatever.
There should also be more optional side- quests and stories blended into the game to make for more freedom and immersion. Cute things like helping an old woman find her lost Purrloin, or scary things like exorcising pesky Ghost Pokémon from a haunted mansion! :3
Anyway, I feel there's a lot they could do in order to make for a richer, more diverse and more immersive experience, without detracting from the staple objective of becoming a champion and beating others Pokémon into pulps. Pokémon has so much potential!