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Yeah, the player character is made out to be a prodigy on Pokemon battling earned through effort.
A lot of character dialogue shows that people underestimate the player and/or are surprised by their skills. Most characters don't have full teams either because contextually, the more Pokemon you have, the harder it is to care for and train them all.
Most people in-world aren't dedicated Pokemon trainers, not even evil team grunts, and only a select handful are actually considered to be skilled/hardcore/professional. While the player character is actively working their way to the top, they're mostly fighting hobbyists.