Have you ever "out grown" a type of game, because it focused on characters younger than you?

Absolutely, I pretty much feel the same way. The only reason I know anything about the Persona series is because I watched 2 guys older than me play through it and riff on it. No way I could make it through on my own.

Yeah what the OP stated is one of several reasons I don't think I'd ever play Persona 5 (I squeaked through 3 back in the day, but that was awhile ago).

I've never felt this way. When it comes to any media with teenage characters in them, obviously most of us aren't going to relate to being in school or having our first crushes like them, but they're usually emotionally developed enough that they'll go through the same kinds of experiences as us: Love, learning, heartbreak, fear of life decisions, growing as a person, etc. In fact, because they're teenagers and experiencing many of these things for the first time, it often allows for characters to more overtly work out who they are and convey a strong sense of a relatable person through that.

Agreed very much. Even if we can't relate to it as something that is happening in our lives *now* usually you are within arms reach of something from your past, or perhaps there is a high level similarity. This makes the emotion / situation the relatable aspect, rather than the person; this can be a powerful achievement when done well in that it communicates a sort of "togetherness" (i.e. you are not the same as this person in detail, but they are human like you, so the same, in broad strokes) and that in turn could allow for acceptance of others that is really quite interesting.

Not really. Night In The Woods was the last example that really pulled me in emotionally and it's just a bunch of teen characters. Granted, they were animal people, but still.

Admittedly I can't think of that many games where I would've played a way younger character as of recently...Ellie in The Last of Us? She was a great character.