This one's a little ranty, but in a good way.
As I'm touring through the RPG scene, I see a lot of people looking for a game to try with their kids. And I'd love to recommend Adventures in Oz: Fantasy Roleplaying Beyond the Yellow Brick Road, but as they go into detail, I realize that AiO isn't the game for them. Because they explain that they've already taught their kid how to play a boardgame, and watched the youngster play video games. And so, they're now looking for some game to provide the "next step" towards roleplaying.
I find this incredibly irritating. Because there are two different parts to a roleplaying game: The roleplaying and the game. These parents are trying to start with a game and then add roleplaying. I can understand at least some of why they do it. By focusing on the game aspect, a new player can still have fun with the game elements even if the roleplaying doesn't really take off. And also, it's often how the parent learned to play. Remember that D&D spent some time as a revolutionary miniatures wargame before it was acknowledged as the father of RPGs.
And they're really selling their kids short. Because if there's one thing that kids can do even better than grownups, it's imagine. And that's the heart of roleplaying right there: Imagining that you are someone else, in some other place. So instead of starting with a game and treating roleplaying as optional, why not make it the core of the experience?
And one of the other downsides of this "game first, roleplaying second" view is that it tends to emphasize combat. Sample scenarios are often just a gridded battlemat with some terrain on it, some "bad guys" and just enough backstory to justify why we shouldn't feel bad when the bad guys fall down and don't get back up. And is that really what we want to be teaching our kids?
Why not teach our kids to be creative problem-solvers? Let's teach them more than how to choose the best weapon. Let's teach them that weapons aren't the only way to solve problems. If you're doing this in the games you run for your kids, whatever rule system you use, more power to you! I just happen to think that AiO supports imaginative play very well.