Over time, as an app developer and a parent, I've come to appreciate the home button just as it is. As an app developer, it means my app will be rated and compared to other apps based on user experience for the child.. how engaging is the app, how much replay value does it provide. If the mechanics are frustrating or the content is boring, children will always vote with their finger and move onto another app. As a parent, I like that developers have to surpass a certain usability and experience threshold before parents are satisfied with the app and provide a good review.
Thats a fair point, but it doesn't really work when you're watching a movie - and my kids attention spans usually don't work so much that way.
My 18-month old will push the button just because he's experimenting with the device - this means instant dissatisfaction for his big brother, watching the movie (or playing an app) with him.
I think there is validity to the idea that you should be able to turn the touch interface off completely. Many apps exist where interaction is not only not necessary (movies), but often-times potentially very destructive to the use case (GPS/navigation).
Its true, though, that its up to the app developers, and having UI-navigation controls be 'staged' with phases and states is probably the best all-round solution. Still, I think it would've been nice to Apple to consider the case where you really, really don't want the app - or movie - to be interruptible.