"We should start from the fundamental question: why should this guy pay more than Joe Schmo at all? Why shouldn't the tax bill be spread equally over everybody, so it's (say) ten thousand dollars per head? That would be what I call "fair"."

Let us leave aside "fair" or "unfair" for a moment.

The problem with a poll tax is that you can only raise the amount of money you can charge the poorest people you are taxing multiplied by the number of people you are taxing.

A tax scheme that operates on a percentage of income (or even increases that percentage as income increases) allows the government to maximize its income in the same way that having higher margin 'premium' products and lower margin "economy" products so rich people can pay more and poor people can pay less allows a business to maximize it's income.