I thought right-hand rule with Z up as thumb was standard in science? You usually project on the xy-plane, for example when calculating the distance to objects on a flat surface.
TBH I'm not sure I totally understand the question but projection is very useful to decompose the orientation of elements, like a cylinder that you just measured with a machine or a scanner. The coordinates and orientation (angles) can be projected in the three main planes XY, YZ and ZX.
Ugh, when I have to open CAD for a project at work I have to setup a new coordinate system with Z going up, every time. The engineers just work with Y up for some reason. Too lazy to change it perhaps? Solid works and Inventor default Y up? I'll never understand it. I definitely understand this meme. There's also models with an origin 10 feet off in X and 20 feet out in Y. I just do not friggin get it man.
That's not true though. While there isn't a standard, convention is to have z up in mathematics, as z is extending the xy plane we normally work with into a third space.
What I can't get is imperial measurement system. Apparently, nobody but americans can
I'm not American but I've been living in the USA for ten years and I still have trouble with imperial measurements. It's painful dealing with fractions of an inch instead of millimeters.
CAD used to be digital abstraction of the physical media that is 2D drawings on paper, so XY is the plane of the paper going horizontal/vertical, and most detailing are in vertical cross sections so Y ended up being up most of the time.
The Z axis is then Frankensteined into the existing system to get a proper 3D representation, so it became the depth axis for the existing XY plane.
In Minecraft it's even more evident as Notch Frankensteined the Z axis into a game engine that's originally developed for side scrolling.
In robotics I use right hand coordinates with z up. So a car is moving in the 2d xy plane and z is the optional third component. This makes sense to me. For some kind of painting on the screen I can understand why you use y as up. Then again, I know these as uv-coordinates.