You're ignoring FICA, which makes up almost as much of Federal revenue as the income tax, and is hugely regressive.
I don't "blame everything on the rich", but I'm amazed at the whining that they do, considering they are getting more and more for doing less and less every year. Considering they seem to make an ever-increasing share of the income, it isn't surprising that they pay most of the income tax. The question is "why do they make so much more than they have historically, compared to the rest of us?". Much of the reason is that they are getting better and better at stacking the deck in the favor of capital over labor.
As a percentage of revenue, corporate profits are at record highs, while wages are at record lows. The actual Federal tax rates that corporations pay have fallen to multi-decade lows as well.
Labor unions have been steadily weakened by legislation all over the country, capital is taxed at more favorable rates, and the bankruptcy laws have been re-written to protect the interests of the wealthy. These are just a few of the many changes that the uber-wealthy have had written into our laws to stack the deck.