I was in a program in middle school where you skipped 8th grade but not every middle school had that program - I don't know if it exists anymore.
And you're right, the fact that a lot of the Asian students who crack the SHSAT are in the low income bracket, would mean that particular system wouldn't work too well in NYC.
Chicago has a much smaller, but academically comparable, system of public magnet high schools. But the schools reflect the makeup of the city better because admission takes into account middle school grades and census tracts, not just the test score.
Almost every student taking the test has straight As. Being from an upper income area mean there are schools (Walter Payton for sure) where you must get an almost perfect score ( greater than 99 percent I believe from what my friends dealing with selective enrollment this year tell me that if a kid got more than one wrong this year it knocked you out of contention for Payton) where student In the lowest income track could score about an 80 percent and get in.