There are “shareholders” only in for-profit hospitals. There are “stakeholders” in all hospitals and schools, etc. As a stakeholder in my local hospital, I’d prefer it to be run by a gifted administrator and use their money to hire a gifted surgeon or oncologist.
If you want to keep disadvantaged, lower-income and under-performing students out of your school, all you have to do is live in a community that doesn’t have any of those, and place your school far enough from the towns where those people are that their parents can’t afford to drive them.
I grew up in such a town. Orinda, California. Miramonte High School, class of '78.