One thing to recall in all this is that heel height is relative to the thickness of the outsole. Many of the high heeled shoes of the '70's had a one inch (or more) thick sole under the forepart of the shoe--effectively reducing the apparent heel height by one inch.
The same is true of many brands of running shoe, although to a lesser degree.
Also heel height is not measured from the ground to the top of the "rand"/heel seat running around the back of the heel. Because that measurement includes the thickness of the outsole.
Nor is it measured at the back of the heel. Some lasts incorporate at "degree" in the heel--a slant or incline that leaves the back edge of the heel higher than the "breast" of the heel. Below 1-1/2" that incline is considered orthopedically problematic because to one degree or the other it takes the weight off the os calcis and forces weight into the metarsal arch of the foot.
Heel height is properly measured at the breast of the heel...directly under the weight of the body.
Good points. While not correct terminology, I prefer to talk about "height differential" of a last : the elevation of the heel when the last is in proper upright postion with ball on a flat surface. This is important especially for womens' shoes that can have platforms of an inch or more. Also I always find it strange when I see typical shoes delivered with half soles that have no additional compensation at heel stack and where last differential has clearly not been altered. Makes the shoes look unbalanced with improper toe spring. I don't know how a manufacturer can justify offering such an incomplete option?
I assumed above however that we were all talking about apparent heel height.