Why does Alton Brown call for three types of milks in a recipe? I'm looking at the ingredient list for Alton Brown's aged eggnog recipe, and I see the following:

1 pint half-n-half
1 pint whole milk
1 pint heavy cream


Does the half-n-half play any specific role here?  

I calculated the final fat ratio of the mix and it's ~20%

Wouldn't it be easier to just mix milk and cream to get the right ratio, skipping the half-n-half altogether?

By my math that's 3.25 cups of milk + 2.75 cups of cream.
The main purpose of the one part of Half-and-Half is to aid in homogenization of the one part of milk and one part heavy cream.

Per this article (toward the end):


  Half and half is also a good solution for desserts that call for equal parts milk and cream, but have a tendency to separate. The fat has been homogenized in the half-and-half, so using it in desserts like panna cotta will deliver a smoother, more consistent result. 


The half-and-half also enhances desired texture/mouth feel properties.