The standard GOP narrative involving corporate tax rates is that if you reduce the rate, you will increase business investment. The Economist divided the OECD countries into four quartiles based on their corporate tax rates, highest to lowest. They then looked at the relationship between the level of the corporate tax rate and bot business investment and corporate tax revenue - there is not much of a relationship. See chart.
Some features of corporate tax rates - first, differences in rates can cause some companies to shop around for the best rate But other factors determine company location besides tax rates (supply chains, transportation access etc.). Also, the highest corporate tax rates tend to be in resource-rich countries. Natural resource extraction creates captive companies. Why don't we just eliminate the corporate tax rate altogether and just tax shareholders directly? First, many shareholders like pension plans are tax exempt. Also, eliminating the corporate tax would give incentives to individuals to incorporate themselves.