I was thinking about something very similar.
like, the teachers will get a lions share of the fee.
this will instantly motivate teachers to better themselves, and move the school away from for-profit model.
but there are some real problems to solve. like, 1. how to get such school started ? who will provide initial capital ? 2. even if such a school is started, how to stop it from becoming for-profit again ? 3. is there a healthy balance between 'for-owers' and 'for-teachers' model ?