Amazon Prime streaming is more than enough for children, and most families already have it.
And the kids don't care at all who they get the shows from.
I expect Amazon to continue to aggressively compete in this area, not to mention Apple and someday, Google. Netflix is giving away their core advantage -- a huge content library and DVD/Blu-ray backup for anything not-yet streamed. No one else has that. Now they're just like everyone else.