I've been playing since I was 5 and have never liked the idea of a child traveling around with monsters and participating in the events included in the games, so being an adult myself right now doesn't have much to do with it. But it's definitely personal preference in the end. I don't think it has anything to do with the story if people you battle end up saying "oh I was beaten bad" instead of "oh beaten by a kid." Those little things, otherwise they basically treat you as a teenager, someone who is around 16 to 18 except for the fact you know you're between 10 and 11 years old. I think Ophie is going into it as if age has a lot to do with the story of the games when in fact it doesn't really have much to do with it. All you have to be is a fresh trainer and you can go through the story in the exact same way, except it'd make a lot more sense.
I would argue that it does matter that the player characters are young. A key part of any Pokémon story, right from the start, is that enemies and allies do not initially take you seriously, which is a more believable reaction when confronted with a young person than confronted with an adult, even a young adult. And because they're minors, they're not tied to a job or expected to have one. (They also seem exempted from school, but that's a different matter--schools DO grant long exemptions from this in real life, but jobs, being a different set of relationships and money-related, won't.)
In addition, all main series Pokémon games are adventure stories. Part of the point is that the player character is seeing new sights, new Pokémon, and new people. As they take familiar urban settings, it would make more sense for a child or teenager to go adventuring.
If the character is an adult, the more believable scenario would be that they're going into a Pokémon-related line of work, which, if reflective of reality, has to be something that other people will pay money for them to do (even if said people are the government). Again, you don't really see present-day stories of adults wandering off and exploring the world, unless 1) that person's job is to wander off and explore the world (Indiana Jones, Jotaro Kujo), 2) that person is a fugitive (Andy Dufresne, The Phantom Stranger), or 3) they have the financial resources or backing to be without a paycheck or a permanent home for a long time and are in a spiritual predicament (Liz Roberts, Forrest Gump). In other words, whenever an adult becomes an adventurer and a wanderer in a modern-day setting (even with some light fantasy elements), they rarely do so on a whim the way Pokémon protagonists tend to do.