I suspect Greg Mankiw is not overwhelmingly tall. But, by Mr. Mankiws rationale is correct, why not tax being white, or male (after all, they tend to make more, on average, too)? I don't think Mankiw would support that. It might be because, even though it doesn't tax effort, discriminatory taxes that are based on the genes someone is born with would erode government credibility.
On a observartional note, I'm guessing if it were turned over to politicians, democrats would turn it into a short-person subsidy, and the republicans would make it a "tax credit" (which of course would be self-defeating as a redistributional matter since it would subsidize the short people who get paid highly the most). After all "tax" is a four letter word to politicians.
Of course, we all know what would happen here... Since, as conservative politicians point out, the whole financial-housing mess was caused by a law thirty years ago encouraging a small portion of loans to go to low-income homebuyers (somehow taking thirty years to work itself out), we can see the moral hazard here. Parents will deliberately malnourish their children to game the system and increase their chance of being eligible for the subsidy (or avoid paying the tax). Stop taking those prenatal vitamins, honey!