One important benefit of sharply progressive taxation that I haven't really heard much is that it makes the rich a lot less capable of controlling, corrupting, and perverting government with massive legal bribes, I mean donations. Importantly, as well, the middle class has a lot more money to donate to compete with the rich.
With a sharp increase in the progressivity of taxes (all taxes, including state and local), the rich become less capable of controlling and corrupting government, making it a lot less efficient. Thus, the increase in progressivity makes government more efficient, increasing confidence in government along with its performance, creating a virtuous circle of government confidence and performance. At the same time, the rich have a lot less money to fund the right wing propaganda machine, thus it becomes a lot less able to grossly distort people's image of government's efficiency, usefulness, and importance, so again more confidence in government. And this leads to greater public investment and insurance, which greatly increases long run growth and total societal utility, with the gains widespread, instead of only at the top.
It looks like such a virtuous circle may have occurred in the early part of the 20th century. The top marginal income tax rate went from 7% in 1915 to 77% just three years later! This was shortly followed by the New Deal, unprecedented levels of professionalism and efficiency in civil service, and respect for it, a golden era of high and evenly spread growth, the birth of the great middle class, widespread and easy college access, the highest level of college graduates in the world (after a generation of Republican dominance we're down to 11th), Medicare, and Medicaid.
Sadly, with the generation of Republican dominance, the circle has been reversed, from virtuous to vicious. The top marginal income tax rate dropped from 70% in 1980 to 28% in 1988. The rich, with their great increase in wealth, gained ever more control of government, deregulated finance, and much else, lavishly funded a vast propaganda machine to slander government, slashed college aid and education (relative to inflation, population and/or it's fast growing importance in a high-tech world), slashed public investment and social insurance (as always relative to inflation, population growth, and/or growing importance/need), and we've had a generation of tragic decline, with the rest of the world catching up to us or passing us in many key areas. And income inequality has gone through the roof, with incomes for most stagnating or declining for a generation, and a third of the population 18-64 without health insurance at least some time over the last two years. In addition, the right uses it's money-fueled influence and electoral victories to degrade government whenever possible, then they say, see, government can't do anything well, which helps them to degrade it further, and the viscous circle continues.
Cornell economist Robert Frank gives one huge benefit of sharply progressive taxation that's little if ever heard, allaying monumental positional/context/prestige externalities; another big one is preventing the rich from controlling and degrading government.