Remember, those earnings have already been taxed on the corporate level. Taxing them at all is double taxation.
Not at all. Tax #1 is a tax for Intel on the money they earned from product sales. Tax #2 is a tax for investors on the money they earned from the dividend.
Each time money exchanges hands, the government gets to tax it again. Otherwise, you'd be arguing that Intel should pay no taxes, because every person who bought PC's with their processors had already been taxed. Anyone who makes any kind of money is taxed on that money, even though that money came from somebody else who had already paid taxes.