I think you're only half right. Yes, the nominal rate is far from the only thing that determines corporate income tax receipts. But in practice, what you see is that the effective tax rate has been steadily dropping. That is, corporations are more and more profitable, and contributing a smaller and smaller fraction of those profits: https://en.wikipedia.org/wiki/Corporate_tax_in_the_United_St...
You'd need a in depth analysis to really see the impact.
Companies always do something with their profit after tax. Most commonly it's paid out as a dividend (which would be taxed) or used in a stock buy-back (increasing share price and eventually taxes as capital gains).
