We have decades of evidence that this doesn't work. I used to live in Kansas where the governor made a priority of his "March to Zero" on taxes, as a guaranteed sure-fire can't-fail way to make businesses happy and lead to more investment in business in the state, more businesses relocating there, more jobs, etc.
And it was a complete and utter failure. It is now in the process of being repealed by people who were left with no choice other than to admit it failed. It is time for people who advocate this to understand that while it may sound great when deduced theoretically from first principles, it does not work in the real world.
State rates are a small factor in corporate decisions, but not an overriding one like Apple's decision to leave hundreds of billions in Ireland, or to repatriate it and pay 42% to California and the US government, to pay the remainder to shareholders to pay 20% more taxes on.
One big example: the elimination of taxes on business income did not suddenly result in much more efficient taxation, scrupulous payment of what was owed, and a boom in investment and expansion of businesses. It resulted in everybody and their brother scrambling to reclassify their personal income as the right kind of business income, in order to pay less tax. Revenue fell off a cliff and the state's deficit projections soared.