There's a better argument for eliminating this deduction, or at least changing it. One problem with it is that some types of local services are provided differently, and therefore subject to different tax deductions. A good example of this would be garbage collection. If I live in a town where my garbage collection costs are paid through my municipal taxes, then this is effectively a deductible living expense for me if I itemize on my Federal taxes. But if I live in an area governed by a homeowner's association and my garbage collection costs are covered by my association fees, then I can't take advantage of this deduction.
I'd be fine getting rid of the deduction entirely except for the deductibility of state/local income taxes. There's no reason to subject the same income to double taxation.
Quibbling about deductions is missing the point and shows that the battle is already lost. If the income tax is to be retained the only sensible way to do it ant the way that will suck the world’s industries into the USA (if accompanied by severe reduction in regulation) is a 9 or 10% flat tax from the first dollar of income with no deductions at all, no credits, no exemptions. Cutting more people out of the taxpaying segment of the population, as Trump’s plan would do, simply enlarges the constituency for higher government spending and higher tax rates. Bush I knew that and his tax cuts therefore had longer range effects that were designed, to be self canceling due to the increased clamor for more goodies from those who don’t think their net incomes are affected by higher rates.