The whole subject became a topic of study in part because so many of the well-meaning progressive reforms of yesteryear such as rate regulation and price controls led to terrible long-run outcomes for the public interest.
First, an income-tax system with a single rate remains progressive the rich pay a higher proportion of their income than the poor as long as it is combined with a tax-free allowance.
No Republican, not even Ron Paul, is going beyond the status quo to insist that top marginal tax rates must be cut by at least a third (ideally scrapping the current income-tax system altogether and replacing it with a pro-growth, low-single-rate tax system that does not punish saving, investing and entrepreneurial risk-taking as the current progressive income tax does).
Take Bangladesh, a country mired in poverty yet with a fertility rate only slightly higher than America thanks to a progressive family-planning policy.