Everyone has pretty much said what I've wanted to say in regards to age having no bearing to enjoyment, so I'll take this in a bit of a different direction.
The Pokemon Company ITSELF is starting to acknowledge us older fans. What with extensive references to Gen I in X/Y, focusing more on game balance for competitive players, creating Pokken Tournament and Super Bowl commercials... marketing has changed significantly from when it was first released in the 90's, which is what most people are stuck on if they even have this belief. Clearly, the game makers don't think we're too old for the series. Especially in the case of those commercials, since adults of all kinds watch the Super Bowl. We're a large enough demographic to be catered to. Nowadays, Pokemon's demographic isn't just about the kids. I think it's just starting to be considered an all ages type game anyway. This forum alone is grounds for that as well, as it is mostly an older crowd of teenagers and young adults who like to have these sorts of discussions in the first place.