NYC’s tax base is not based on neighborhoods, its centralized meaning people in Staten Island pay lower property taxes than their neighbors in NJ because they benefit from the business taxes in Manhattan. People in Boro Park pay lower taxes because of the real estate in Manhattan. Its not like that in the Suburns. Rockland does not benefit from Manhattan real esate (on a local level, they do on a state level)
As a side note the largest real estate holder in NYC is the Catholic Church (and yes some people do want them to pay taxes). The Watchtower is selling their property in Dumbo worth about $6 Billion dollars tax free. No yeshiva in Brooklyn has any worth even close to $6 billion.
Even though the Frum people in Ramapo do not send their kids to public school, their school cost is not zero as we have debated this ad infinitum (Busing , Mandatory services , etc)
Also the Suburbs have other costs that city residents dont even realize , Like sewers, Police, Fireman, Road repair, Snow plowing, Sewers , Social Services and more because they have a lower tax base and those costs are borne by property taxes