Aloft (Beta)
What do packing height/width actually do?
This is related to how the WoW Client places nameplates on the screen; additional discussion is here.

Adjusting packing height/width actually adjusts the size of an "invisible" frame that the WoW Client maintains for every nameplate, known euphemistically as the "nameplate frame". This is what the WoW Client uses to manage placement of nameplates on the screen (specifically, adjusting packing height/width leaves more empty space around nameplates, at least when the Blizzard standard "Names>Allow Overlapping Unit Nameplates" interface option is disabled).

As far as I have ever been able to tell, the center of this "invisible frame" is hardcoded by Blizzard to a certain point relative to the 3D model for the associated unit, and cannot be accessed or adjusted in any way, and the visible elements of nameplates are effectively hardcoded to the lower center of this invisible frame (though the relative placement of those visible elements can be adjusted via Aloft).

As well, this can affect mouse sensitivity, as described here.

Adjusting the size of this "invisible frame" (via packing height/width) moves the lower center point of the "invisible frame" down, which then effectively moves all the visible elements of the nameplate down (and can also render the nameplate insensitive to the mouse, as described).

So, packing height/width is to control how much spacing around nameplates you want, not the relative placement of nameplates on the screen (though it has side-effects that affect relative placement). If the Blizzard "Names>Allow Overlapping Unit Nameplates" option is enabled, packing height/width are basically ignored by the WoW Client. And, as described, changing the relative placement of nameplates on the screen (through any means) by very much can render the nameplate insensitive to the mouse.