At the state level, higher taxes for the rich may have the effect of driving people to other states. That should narrow the income inequality gap in the states being abandoned, but it hasn't done so in California and other high-tax states in the top-10 gap list.
Hollow demands for exempting groceries from the sales tax make for good policy platform planks, but they don't translate into policy changes. That would require a restructuring of the tax system. A reduction in the state's personal income tax, fought vigorously this year by OK Policy, went nowhere partly because analysis revealed that it would result in many middle-class taxpayers getting a tax increase while those in higher and lower incomes improved their positions.
The income gap is a peculiar obsession. We should focus instead on the gap between what all taxpayers make and what they get to keep and the gap between the cost of government programs and the ability of citizens to pay for them.