The logistics of schools owning a business as a legal entity has some legislative implications. This is a technical question for lawyers, as I do believe there are ways to navigate around it (like certain percentage of ownership...etc)

Overall, the idea is interesting, and could be worth to explore. One suggestion I have is to keep the main focus on high schools, associate degree schools (2yr colleges) and actual higher education institutions, as the dedication, enthusiasm and success rate potentially is going to be higher associated with such entities.
Good luck,
Sincerely,
KT