The case for eliminating the double taxation of corporate profits by creating a deduction for dividends paid, as opposed to an exemption from dividends from income or an imputation system, is as the article linked explains, probably the best way to mostly eliminate double taxation of corporate taxes for publicly held corporations.
The dividend withholding tax credit (i.e. distributing dividends that come with a tax credit for taxes already paid at the corporate level also called imputation) can work in a system with one level of corporate taxation, but can be dreadfully complex in a federal system with corporations that owe both federal corporate income taxes and state taxes in multiple states. A dividend paid exemption distorts progressive income tax rate effects.
A switch would reduce systemic risk created by the existing debt-equity distinction, and makes less complex C corporation taxation viable for many more entities (pass through taxation with K-1s not based on actually distributed profits has all sorts of problems of its own).