State taxes paid are not deductible on your federal return. The only time state taxes are "deductible" is when you file in multiple states. But even then, you are paying taxes in one state, and then deducting them on your resident state return so you don't end up paying twice. (And yes, I know the NYC tax isn't necessarily a state-tax, but when filing, it is somewhat similar)
True, but that is part of the city's tax income model. They lower the property tax in the city, because the people living there are being taxed on their income. Yes, there will be examples of people with no taxable income but own valuable real estate, that is something the city considered (I'm assuming they did) when deciding this is the way they wanted to tax their citizens.
This would be comparable to a state like Texas. They don't have an income tax, but they have a much higher property tax along with a higher sales tax.