Chrono Cross - The Scars of Time

Unless each new playthrough unlocks a lot more content then only fanatics will play it through and through, which may be your goal.

I prefer the freedom to start what I want, when I want, from the start. If that means I can play as the goofball characters in a game - going through some foolish quest that's mostly jokes - then I'll do that if I like it.

You can do a lot with ambient storytelling, especially when the player is distracted by what seems like a lighthearted story. And there's always a way to flesh out any character if you put your mind to it.