@Yakuzaice: Let's put it this way: You have two kinds of toys; ones that are either loud or very loud and they sound horrible. The piano in first video is one of the best cheap toys available, it has decent volume control, it doesn't sound that bad, but it breaks down easilly. And it's priced somewhere above 50€.
The other type of toys are toys that have good volume controls, sounds nice, but they cost a lot (closer to 200€).
Removing batteries is the same as not buying the toy at all. It's not going to intrest the kid anymore.
As for randomly mashing the piano while music plays, is excactly how kids play the toy pianos. They like to "play along".
Look, the idea of "not having specific goals" in Wii Music, is at the same time the idea of playing the songs in your own way. I've already compared it to Guitar Hero, which is basically a rhythm game based on timing, that you can play only in one way. In games like Guitar Hero, you can only "fail" or "succeed", but you can't control how you play it, while this isn't the case with Wii Music, you can't fail or succeed, but you can only play it your own way. Play a random riff in Guitar Hero and tell what it sounded like and you notice the difference.