I mean, it's not like Zavala is sitting us down and going through the ABCs. Also the opening sequence also sets some pretty grim stakes in the world.
Ultimately, I don't know that the aesthetics in Destiny are really kids' show fare as much as pulp sci-fi or maybe in line with Jack Kirby's work in comics.
While there's a fair bit of levity in some sections of the game, I don't buy that it's talking down to anyone or infantilizing the audience? If anything, the fact that there's some lightness to the dialogue in the face of the narrative is kind of needed, y'know? Personally speaking, I've long since grown sick of the grim-dark shtick games have wrapped themselves up in to appear "mature" and I'm old as shit.