You must not ride very fast, I go 30+ down hills into stop signs, I don't know how you would stop in that scenario. New York is pretty flat though, you should try riding break-less in San Francisco, apparently a lot of people do it. I was pretty happy having breaks when I rode there, that city is a lot of fun on a bicycle.
A road bike goes a lot faster then a BMX and you can stop pretty quickly just by jamming your foot into the back wheel.
I do ride in the city with high traffic/pedestrian area but not like a idiot.