What point are you trying to make though?
You're original point is that you wont ever see or interact with the president of the school unless you get in trouble.
I responded with, that's not the case in private schools
Then you said that president operated in a different universe from the students and didn't have any 1on1 interactions
I responded with, that wasn't the case at all in the college I attended
Then you said that a president cannot affect the lives of the students in any meaningful way
I responded with, that wasn't the case at all in Vandy (see on-campus fraternities)
I'm not saying the headmaster is out there changing your grades

I'm just saying he's the face of the school and has influence on policy and the social climate
If there was a private school opened by and ran by a KKK member, none of us would send our kids there no matter how good the curriculum is