People are emotionally averse to firing others they may have been working with for years, and there's not a good enough reason to fire someone in a private orga

People are emotionally averse to firing others they may have been working with for years, and there's not a good enough reason to fire someone in a private organization unless they affect the bottom line, and outside of exceptional cases I don't see how the bottom line changes much based on individual teachers. You're probably not going to quit private school based on any one single teacher. You need a strong economic incentive for the organization in order for the "fire more easily" idea to work. For instance, if a private school got paid according to the competitiveness of the college the student is accepted into.