But taxes on inheritance and investment are totally regressive (and have become even more regressive), which undermines the benefits of a progressive system for earned income.
Inheritance tax, on the other hand, usually has a "lower-bound" that prevents the very poor from being affected.
Taxes on investment? You mean, capital gains? Or something like dividends?
Taxes on investment are complex. Considering the fact that most humans do not have anything approaching a real investment portfolio, it's hard to understand what you could mean when you say this kind of tax is regressive.
A properly progressive income tax should mean that more people can join the investment class. If the taxation within the investment class is actually regressive, then maybe we worry about that when the majority of humans have this problem.
When I think regressive taxes, I think things that are flat fees, or else things like fica, which cut out after a certain income.
What it sounds like you are trying to say is that it's not "progressive" enough for your liking. And then you turn the definitions upside down and label it "regressive".