Are these axis you listed defined by TU or is there an engineering background behind them Vman?
You do actually have a good point.
My background is engineering design, aircraft and automobile. In the car industry, the axes are labeled as quoted in my post, with the vertical axis being Z and the thickness axis being Y.
However, from a machining point of view, the thickness or depth cut is always the Z axis, as per your preference. Because of this difference, I always had to mess about with the axes when I used to do work for Bob LaLonde. It got confusing at times, but we sorted it out in the end.
From a layman's point of view, axes are always X:Y with the third, depth axis being Z, the same as the machinists axes as it happens.