Plus, some of the starting Pokemon might be more willing to battle than others. Like there's one Squirtle that really enjoys fighting to get stronger, but another Squirtle would be willing to help catch more Pokemon because they're a softer battler. Or a Hoenn/Sinnoh Pokemon better suited to contests over battling in Gyms. That's a way to get some personality to the Pokemon characters instead of just the trainers.
But yeah, what RedWing said about the trainer's personality being reflected through their Pokemon choices rings true. Like Gary had a lot of fully-evolved diverse Pokemon on his team and Ash didn't, and through that, you can kind of get an idea of what type of trainers they are.