To pay for the development of children's entertainment. Public television is wonderful but I bet all of us look back fondly on a show that we loved as children that would not have existed without ads to pay for its production.
Look, shared cultural nostalgia is great, and all, but I'm not sure that makes for a good reason to allow advertizing to kids.
I know I cannot already, since I grew up without cable television and had most of my childhood televised entertainment provided for me through public broadcasting and rented/bought VHS. I'll admit that my circumstances were unusual though.
That's not to say good kids' stuff doesn't exist, but I see nothing wrong with just murdering the whole model of Media-Driven Consumption, from food to toys to fashion, in its sleep. With a knife.
It's bad, and society should feel bad for allowing it.