the Pokemon world, every region, is filled with people doing things that aren't Pokemon-centric. there's bakers, teachers, photographers, businessmen, artists, and so on who may own and interact with Pokemon in various ways (like the Orange Islands guy who used his Charmeleon for glassmaking), but never "train" or battle with them the way Ash and Clemont do. I don't believe Serena has to be a Pokemon trainer to belong in the world of Pokemon.
if every female companion of Ash's had been treated this way, just tagging along and doing stereotypical "girl" things like baking and trying to look cute, I'd be over it by now. but in the context of the whole series, Serena is being handled very differently than the 4 girls who preceded her, and I find that refreshing. clearly she's not what everyone wants from the female lead, but as a long-time watcher of the series, I welcome this new approach.