First things first, it sounded a lot like Genius Hour.
I did not understand how it was as if students designed their own schools. The students still had to follow a strict plan of schedules and deadlines. Instead of Genius Hour, it seemed like Genius Day! There was very little difference between the two programs, except for the fact that "school" lasted for the entire day. There was no sense of freedom whatsoever. This new school still had an unchangeable schedule, the same amount of time, and teachers still present. If one wanted to design a school, wouldn't they have the choice whether to have a flexible schedule for the students, or possibly different ways of learning? Instead, the only thing that changed were the subjects.
I'm probably being too harsh on the restrictions. The benefits of having self-taught classes are just as good as Genius Hour's. Cooperation, discussion, independent work, and troubleshooting are certainly good abilities to have. The idea of a student created school is interesting, but to really be a "school", you would really need to have more choices.