It's purely a matter of popularity and install base. If you look at the back catalogue of PS2 games, there are likely as many - if not more - "kiddy" games, but the PS2 is never deemed a kiddy console. It's because the Wii is the most popular console right now, so developers of all kinds are going to flock to make games for it, This does unfortunately mean that it has a large amount of complete garbage, most of which is, admittedly, quite kiddy. But I think you'll find the majority of rubbish games on the PS2 are the kiddy titles. And it's because that's where the money is at. But you get a healthy balance with the PS2 and the Wii.
Don't forget, the Wii has only been on the market for 2 years - it has plenty of time to build up a massive library of all sorts of games. As it stands, it's doing quite a good job of representing a wide demographic.