Admission is by lottery if there are more applicants than places, not by cherry-picking applicants. They hire teachers with subject-matter degrees and experience: they have some PhDs and a couple ABDs (all but dissertation). Half-jokingly they said they didn't look to hire people with teaching certificates, but wouldn't hold that against them. I had a master's degree in computer science and worked summers to get another master's.
The school was smaller (maybe 700 total students K-12; the class of 2022 graduated 26), which right there, I think, made for fewer behavior problems. There was a well-thought-out discipline policy which was enforced by the administration and backed up by the board and most parents. After all, parents had made a choice to not go to the regular district schools but enroll in this school instead.
I agree that the odds are much better for school success with smaller sizes, a focused curriculum (whether it's International Baccalaureate, Core Knowledge, STEM, arts, or whatever), highly qualified teachers, and supportive parents.