The issue, if I'm understanding the OP right, is that income taxes are moderately progressive until you get to the levels where people make their living off wealth, not income. Someone earning a wage is going to pay a monotonically increasing percentage of their income as they move up the scale. That's fine. Someone who owns a holding company that itself owns 80% interests in a variety of LLCs that reinvest their profits to increase their paper valuation, and then takes out loans against the value of their holdings to pay for living expenses - could quite easily end up paying zero tax. Warren Buffett once posted that he pays half the tax rate that his secretary does (17% vs. 34% [1]), and Buffett doesn't even partake of some of the tax avoidance strategies (like taking out loans against his holdings instead of selling them outright) that many other wealthy do.
Up to a certain level you are taxed on what you EARN. Income tax is relatively progressive.
Beyond a certain point you cease to be taxed on what you earn. Instead you are taxed on what you SPEND. By this I mean, you have unrealized or non-repatriated money and you only realize those gains and pay taxes on what you need to cover your expenditure.
So if you gain $100m in a year but only spend $10m then you're only taxed on $10m and the other $90m probably grows tax free until you really need it. This might mean then that you're effectively paying a 4% total tax rate (40% of 10% of your income).
But it gets worse. Because of zero interest rates, there's no point in paying tax on that 10% either. Instead you borrow $10m at 1.5% interest secured by your unrealized gains. If your unrealized gains grow at more than your interest rate you're coming out ahead. The worst case is you're deferring your taxes for years. The best case is you're effectively deferring them forever, or at least until interest rates increase to the point where realizing the gains is cheaper than borrowing.
This is correct. Piketty's research has shown that as one moves to progressively higher echelons of the wealth distribution (top 5%, top 0.1%, top 0.01%), a higher and higher proportion of capital is accumulated through returns on capital rather than income. That being said, we shouldn't discount that while taxes on income are more progressive than taxes on wealth, they're still significantly less progressive than those of most other Western countries (and we have significantly higher levels of income inequality compared to those countries.)
[1] https://www.forbes.com/sites/paulroderickgregory/2012/01/25/...)