In my field of awareness, there has recently been more discussion than usual about deductibility of constituent-state taxes and of municipal taxes from income computed for purposed of Federal taxation. I think that most of the discussion has been fundamentally wrong-headed.
In the textbooks of middle-schools, of high-schools, and of introductory courses in college on civics, on politics, or on economics, there are discussions of various proposed guidelines for taxation, based on ostensible or insinuated theories of justice. One commonly offered theory is that people should be compelled to pay based upon supposed ability; another is that they should be compelled to pay based upon the amount of services that they receive from the state. I've yet to see such a discussion in such a textbook that could withstanding much critical examination.
In any case, these homilies don't serve to explain how-and-why taxation is effected in the real world, except in-so-far as some of their prescriptions are invoked to argue for a tax of one sort, even as conflicting rationalizations are offered (often by the very same people) to argue for taxes of other sorts. Historically and to the present day, taxation has been fundamentally opportunistic. That which has been taxed is whatever seemed to be most readily taxable. Targets of convenience have been wealth or income that has been thought to be easily tracked and measured, difficult to relocate outside of the jurisdiction, or for the taxation of which there is wide-spread acquiescence if not support within the community. (It is with respect to that last aspect that textbook theories have their real relevance.)
The state is not satiated by some steady extraction of wealth from the community. When extractions are greater than were expected, the state will not return the surplus to the taxpayer as such, except under extraordinary pressure; and, here-to-fore, states have always moved towards attempting to extract as much tax from their communities as the communities will suffer. This tendency is natural, as the people who make-up the state generally see their positions within society improve as they have increasing command over resources; mechanisms that exist in sectors whose rewards are determined by markets which cause participants to identify and pursue efficiencies simply have no correspondents within the state; the state is able to cultivate dependencies in the wider population; and many people imagine a very extensive rôle for the state within society (especially those people who lose sight of the distinction between the state and its subjects). The state grows ever larger and becomes ever worse at the allocation of resources, and so seeks ever greater extractions.
When, within the jurisdiction of a constituent state or within a municipality, there is greater community resistance than elsewhere to taxation, there is less taxation than there otherwise might be. That difference is a target of opportunity for a federal state, whose jurisdiction encompasses a wider community. There is a mechanism for obtaining the acquiescence of that wider community without typically triggering a significantly intensified resistance on the part of the communities subjected to a federal surtax in the face of lower taxes by other entities. That mechanism involves allowing taxpayers to deduct what taxes they pay to those other entities from the calculated worth of something that the federal state taxes; because, in the face of those deductions, parts of the wider community become less resistant to rate increases.
Let's say that people in jurisdictions A, B, and C, which are all of roughly the same size, face a federal tax of 30% on income, and that people in jurisdictions A and B face a more local 10% tax on pre-tax income, while people in jurisdiction C face a no such tax. If the federal tax is increased to 1/3 on taxable income, but local income taxes are made fully deductible, then the people of jurisdictions A and B face no net increase in income tax, and so may acquiesce; the people in jurisdiction C may thus find themselves out-voted and their taxes increased by about 3%.
A great many people imagine what thus happens is that, given deductibility of more local taxes, people in jurisdictions with lower local taxes are force to subsidize those in jurisdictions with higher local taxes; but that conclusion is spurious. It would in some sense follow if the quantity or quality of goods and services delivered by the state were well correlated with the amount of resources that it extracts from the community, but there is no such correlation, except in transitory cases in which the state deliberately impairs performance to provoke acquiescence to greater extractions. The people paying lower taxes than they otherwise might are not getting something from those paying higher taxes than would be tolerated without the mechanism of deductibility. They are simply less victimized. One would be no less mistaken in claiming that people who live in other nations with lower income taxes are ipso facto subsidized by American taxpayers.
(For purposes of economic analysis of some sorts, tax-cuts and subsidies are equivalent, but those in the jurisdictions that are less taxed by the federal state have not received a tax cut, they have instead not been subjected to tax increases imposed elsewhere. And the aforementioned equivalence holds only if either there is no prior property in resources, or the state has a prior claim on whatever resources are involved. If no one has a claim prior to taxation and subsidization, then no one is paying taxes; they are being extracted from resources that are un-owned. If the state has a prior claim, then there are again no tax-payers; there are people who are granted more or less wealth or income belonging to the state. And, if there are no tax-payers, then the tax-payers subsidize no one.)
Eliminating the deductibility of other taxes would create greater resistance to federal taxes, as some who had previously not been subjected to higher levels then would be. But not everyone thus penalized would previously have been a supporter of imposing those levels on others. Innocent by-standers would be dragged into a fight; there could not be justice in that.
 When I say
state, I don't necessarily mean one of the constituent states of a federation such as the United States. I certainly don't mean the jurisdicational area of one of those states, nor the inhabitants of such an area. A state is an organization that successfully claims an effective monopoly of some sort in the control of violence.