your definition of "actually a school" seems to arbitrarily include a lot of reporting and paperwork and commerce that have nothing to do with the bit where you teach people stuff
Education does not operate in a vacuum. Many students are incentivized by the social accreditation of completing a program. Institutions need some way to qualify that teaching is actually being done. Whether it be an examination, a certification, or bringing a project to completion.
your definition of "actually a school" seems to arbitrarily include a lot of reporting and paperwork and commerce that have nothing to do with the bit where you teach people stuff