Perhaps more importantly, corporations effectively form "unions" for wealthy people, which are an effective unit for lobbying. Jeff Bezos, for example, only owns something like 15% of Amazon...but he gets to use 100% of Amazon's resources to lobby the government and try to sell government representatives on the idea that what's good for Jeff is also good for Amazon's employees and the American public. Shift those taxes to personal income, and all of a sudden that sales pitch becomes a lot less convincing.
Without corporate tax, wealthy business owners probably won't pay any tax at all. They'll just pay themselves with absurd benefits from company accounts.
Or perhaps, just endlessly take out loans against their ownership stake. No taxes if you never pay them back