"It's simply not necessary for children to do homework."
No, it's not but it reinforces classroom work and encourages children to read beyond the work done at school. Thinking back, there's a lot I know that I didn't learn at school but did learn as a result of school. My parents were intelligent and hard-working but they wouldn't have had the knowledge or backgound to be able to stretch my my mind in the way my teachers could.
Are you sure that this country is any more dumbed down that it ever was or do you just read about it more? We have a cult of celebrity at the moment and stupid people are all over the media but I don't think that means there are fewer knowledgable people, just that we don't hear so much about them. Another thing to bear in mind is that what you were taught in school is no longer so relevant - do we need to know about the classics and fine art to get on in the world? No, we don't. It's nice to know but not necessary.