Child's Play, and a Metaphor for Game Design?

So, I was watching two young sisters play -- a 2-year-old and a 4-year-old -- and I was struck by the dynamics of their overlapping, conflicting make-believe.

2-year-old: "I Clifford! Big Red Dog!"

4-year-old: "No, you're Emily Elizabeth!"

2-year-old: "I Clifford!"

4-year-old: "No, Daddy's Clifford because he's big and I'm Cleo and Mommy's Jenna and you're Emily Elizabeth."

2-year-old: "I T-Bone!"

4-year-old: "You can't be T-Bone. You're a girl."

2-year-old: "I Mac."

4-year-old: "Mac's a boy. Emily Elizabeth's a girl. You're Emily Elizabeth."

2-year-old: "I Cleo. Cleo girl."

4-year-old: "I said I'm Cleo. You're Emily Elizabeth."

2-year-old: "I Clifford! Big Red Dog!"

I think there's a lesson in there somewhere, not just for life, but for the smaller part of it that is game design.

Generally, I don't like to be told what I'm going to be in a game (faceless space marine/WII soldier/uninteresting bouncy platformer thing/etc.). I like it to feel organic -- which means I can't tell that I notice I'm a character, but I'm totally into it and feel empowered by it.

I'm trying to figure out the formula, mainly by looking at games that have strong types of characters, do it well, but I didn't notice (Halo, Namco's seriously under-rated Breakdown, Half-Life, etc.).

I'm also thinking about games that didn't work for me (Brute Force, Perfect Dark Zero, Stubbs the Zombie (great game, but I wasn't Stubbs -- I was playing Stubbs), etc.)

I'm playing a lot of Tecmo's Dead or Alive 4, and I'll be writing separately in my "I'm Playing" blog about it, but I'm wondering if this is one of the strengths of a good fighting game -- to finish the game, you have to play as a ton of different characters, and you have to "get" all of them. And they're all different (in a good fighting game).

I need to think on this some more.