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I'd love to see this whole rival thing in a different standing or something a bit more unique? Maybe a game where you actively fight or support your pokemon in battles so that whole "Your trainer cares and loves their pokemon" angle is a stronger theme? Think a Trainer Class system that gives passive bonuses to your Pokemon while in the regular game, thus making it so your bond with your Pokemon is not only tailored around petting and feeding them, but their builds and activities you do with them outside of battling.
Imagine, your Trainer can become say a Aroma or Flower Trainer with a heavy theme around Grass Types and they give bonuses to Grass Moves, Sunlight stuff, and Powders. Or an Aura Trainer that boost Aura moves.