I was assuming that places such as Flushing and Harlem were already place=suburb given the even more local neighborhoods within them. But apparently they’re already place=quarter, so I guess there’s no existing conflict. Personally, I’ve tended to use place=suburb for parts of a city that used to be smaller cities before they were annexed and have retained their distinct identities. This could describe the five boroughs, but at a different scale perhaps.
Nominatim seems to equate place=borough with place=town in some contexts and place=suburb in others. 