Rich people pay most of the income tax?
This is a humbug because the payroll tax is a capped, flat 16% income tax that is paid on every dollar of income by the working class. Even people with an earned tax credit pay 8% because their employer's half is not returned and it comes out of their total compensation package. The payroll tax goes right into the treasury and is spent for current budget needs same as every other tax.
Social Security is a universal welfare system and there is no legal connection between SS and the tax. Why no connection? Because Congress could repeal the SS benefits.
Second, very rich people don't pay income tax. They have very little income except for dividends and interest payments. They pay 15% capital gains on the money they draw for personal expenses. When Bill Gates was CEO of MS he was regularly reported as being the worst paid CEO in western Washington. He didn't need to draw a salary.