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They did not, because of the different needs of the different mediums and the series debuting on the Game Boy. But for a world that revolves so much around these amazing creatures, they are awfully absent in the games outside of the battle screen. The games do have length and level progression to consider in ways other media don't have to, and you want to avoid the pure filler that can make JRPGs overly long piles of episodic nothing, but episodes like Snorlax blocking bridges or Rotom being funny in the Old Chateau should be more frequent.