I agree that when marginal rates were higher, there were more deductions to offset income. Those were cut down dramatically by multiple layers of tax reform. So whatever deductions you feel the tax code is still full of, there are certainly far fewer than before. And the wealthy pay higher marginal rates and higher average rates than the rest of us, according to the Tax Foundation. So all those deductions for the wealthy you see are not sufficient to reduce tax rates and relative share of tax paid below those of the non-wealthy.
Secondly, lower income folks have been largely removed from the federal income tax rolls. 40-45% pay zero income tax. So when evaluating relative tax burden, you have to recognize federal income tax is zero for a very large swath of the population. Prior to the multiple rounds of tax reform, even lower income folks typically paid federal income tax.
Warren's statement, though provocative, was probably false. He probably makes most of his income as dividends and capital gains, which bear a lower tax rate than wages on average (because capital was previously earned and taxed). But as a high earner Warren probably still would have an effective rate much higher that his secretary since the top capital gain rate is a flat 20% plus the 3.8% rate on net investment income of high earners. So call it 24%
If his secretary's income put her in the top 25% of all taxpayers, her average effective rate would be only 17.1% according to the Tax Foundation.
https://taxfoundation.org/publications/latest-federal-income-tax-data/