see https://www.pewresearch.org/short-reads/2023/04/18/who-pays-...
income tax is progressive but tends to become regressive at the very top when individuals have control over what counts as "realized income". The ultra wealthy in fact don't pay so much tax (and certainly not their "fair" share).
What you say is true absent any tax optimization, alas there is such a thing, especially at the top. Also, see works of Zucman and Saez.