At an aggregate level, this argument makes some sense. But when you look at individuals who pay lots of tax, there actually is a good reason to allow a deduction from a tax policy perspective.
States like CA and NYC have progressive income tax rates, so the people paying a lot (and whose deductions are being capped) are high-earners. If their incremental tax dollars were being used to essentially fund consumption-like services for high-earners, then it would be proper to deny a federal deduction. The argument would be: well, your state took taxes from rich people in order to fund fancy museums/opera houses, so we shouldn't allow a deduction for this sort of state-intermediated consumption.
But CA and NY's high-earner taxes aren't used for this, for the most part. For example, CA's "millionaire's tax" (Prop 63) is specifically used to fund state-provided mental health services. Presumably none of the rich people who fund this actually receive these services because they already have their own doctors.
Of course, these taxpayers do see an indirect benefit from the provision of social services, insofar as they help keep crime rates lower and such. But in general, the income taxes paid by high earners are not akin to consumption, which would be the tax policy argument that one would make if trying to get rid of the federal deduction.