Children attention span is very short and can't stay seated for a very long time, they will want to get out of their seats, play with toys and a number of things that can disturb others who just want to relax and enjoy their flight, and parents' peace of mind.
Children's attention span is very short. They would rather get out of their seats and play with a toy or even complain for things that they want, and this way parents can keep a closer watch on their kids, by having sections that are just for kids, without any disturbance.
I'm bringing my baby on a plane, I'm going to make sure that I can do what I can to make it a smooth ride. I've been on planes before without a kid, and I enjoyed the quiet. I actually prefer that parents pay a little more to sit in a parents zone. A place near the restrooms for accidents and the walking room to calm a crying child. A place set farther back so I/they wouldn't annoy anyone. Travelling with kids isn't easy, this might help a little.
A child is a person, same as an adult. It isn't fair to charge a parent more for their children. I do, however, believe there should be some more child friendly flights. There should be a section of the plane specifically for children. Not the private area, but perhaps an area closer to the back.