Corporate taxes don't pay for schools in the US. The bulk of school budgets come from local taxes like property taxes.
In NYC, the "fat cats" pay the vast majority of such taxes since they own the most expensive properties (both commercial and residential). Also, those same people, to the extent they have kids in school... send them to private schools. So the rich in NYC pay for the schools and don't use them.
Of course unskilled "set dressers" at places like Lincoln Center can make well over 300k a year, so technically they are also "rich." (easily in the top 5%-10% of wage earners). Course in the city that's not enough to own a terribly expensive house, so they'd not be paying as much in property taxes as a guy with a 3M$ house (from watching that "Selling New York" show, looks like for anyone with kids, high 2 millions is pretty much entry level for anyplace worth living).
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"Government, even in its best state, is but a necessary evil; in its worst state, an intolerable one." — Thomas Paine
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