Excepting star-power labor (professional athletes, entertainers), most of the income in the upper tax brackets goes to the owners of capital. When stocks pay dividends, the dividends are taxed as income. If you raise taxes on upper-tax-bracket income, you just promote stock-based compensation instead: compensation in stock options (which are taxed as capital gains when realized, not income), stock buy-backs instead of issuing dividends (again, capital gains rather than income), etc.

The long-term capital gains tax rate, for those in high tax brackets, is 20%.

Go ahead, set the income tax rate for high tax brackets to seventy percent. It won't actually make a difference.