Do you really want me to go over the game and show you why the parts involving the Disney characters were the least childish ones?
KH1 Triton was semi epic and dramatic.
Mulan's world? Soldiers turning into Heartless? Sora having to deal with people hurting people? Fantastic; loved every minute of it.
PotC by definition isn't childish.
Monstro? Sora and Riku reached the conclusion they should be at each other's throats. Father and Son separated, child-kidnapping.
Neverland? What was childish about that? We're talking about friendships breaking to pieces and people losing their minds (in KH terms but still).
I can go on, but I don't see the point. Most of what you're refering to are Donald, Goofy and Mickey specifically, but they too have their moments.