What if we had a tax based on height?

I was just reading this paper by Greg Mankiw. In it he says:

The empirical leg is that a person’s height is strongly correlated with his or her income. For example, Anne Case and Christina Paxson (2008) write that “For both men and women…an additional inch of height [is] associated with a one to two percent increase in earnings.” This fact, together with the canonical approach to optimal taxation, suggests that a person’s tax liability should be a function of his height. That is, a tall person of a given income should pay more in taxes than a short person of the same income.
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Case, Anne and Christina Paxson (2008). “Stature and Status: Height, Ability, and Labor Market Outcomes,” Journal of Political Economy, 116(3), pp. 499–532.