My daughters went to a school like that in TX -- over 4000 students. I dug deep and came up with the $$$ to send my sons to a private, Jesuit College Prep (about 400 students at the time). Best decision I ever made. It was too bad that there was not a comparable slchool for the girls, but they were AP students and in a closed environment, so they did OK.
When it was time for college, I had a hard time in TX finising a college larger than the HS. At the time, TX was full of teeny, tiny colleges and gigantic Universities.
You are absolutely right that that staff did not know the child and really didn't care at all.
Funny thing, the regular curriculum at the Jesuit Prep School was stiffer than the Advanced Placement curriculum at public school. And, at Jesuit, the Principal knew your name and a lot about you before the first week was over. My sons couldn't slack off and hide there.
I believe I had a better education by 7th grade than most of the public HS ‘graduates. And this from back in the day before the FedGov became the 800 lb gorilla..