I often carry my 6-year-old (just a week ago, before that I was 5-year-old) daughter on a bicycle frame. Plus, my wife has mastered this science, and it turned out to be just the thing for kindergarten... I looked at children's bicycle seats - both expensive and not so good.
The main problem, as you might guess, was in the attachment to the frame. Even when riding with a child’s butt directly on the frame, the rear brake was no longer fully functional.