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Story-driven for Pokemon is typically too self-contained. There are too many one-off characters so that no actual story ever really gets carried out, G/S and B2W2 pretty much the only exceptions. (XD as well but who's counting..) So you'll end up with supposedly important characters like the Elite Four not really making an impression on you because they talk to you before a battle and after a battle and that's about it.
That's why we have to get hype about recurring characters. Even something simple like a battle fodder NPC on a Route mentioning a Gym Leader from another Region counts as story for this series, and inconsequential cameos can end up critical continuity moments for the series.
Looker by simple virtue of appearing in more than two games is going to end up having one of the longer Bulbapedia articles.
I don't know what GF thinks counts as a story. It'd be interesting if, for example, the Aether Foundation was using Infinity Energy to open portals to Ultra Beasts, given how important Infinite Energy was to ORAS, and in ORAS it was in turn a reference to XY's two-sided pamphlet of an overall plot.
I wish it was more story-based, but I wouldn't worry about that rep's line. It means nothing.
