NYC students, in general, have no discipline. I went to a public high school in NYC and everyone is stupid as a rock.
I used to do afternoon tutoring for high school students when I was a senior in my high school. Nobody cares about learning and they only show up for answers.
People like that do not belong in the specialized high schools. SHSAT isn't a test of intelligence, it's a test of discipline, because you better invest the time to open up a book and study for it.
I went to public school in NYC as well and I will say that the lower program in the school was like what you're describing, but the highest program did have intelligent and disciplined students.
Apparently after I graduated (and my class), they told us that we were the last "smart" class to be there and James Madison High School is now a shitshow. ---