I have to say that the NYC schools are a different monster altogether.
Instead of most kids who are stuck in neighborhood schools, the smart ones can take the subway to Bronx Science, Brooklyn Tech or Stuyvesant. It works against the awful move against tracking in schools.
In any case, schools are becoming more legalistic and I would have to guess Klein was put in mostly to negotiate contracts.
NYC education is pretty much an all or nothing game for kids. If you can afford the $20,000 to $30,000 a year then you can get a good education. Ditto for bright kids who go to the specialized schools -- the ones you mentioned, as well as schools like Performing Arts, Art and Design, Fashion, etc.
However, if the you're an ordinary kid with average grades, etc. then you're pretty much kicked to the curb.
Oddly, the same model holds true for employment.