In school, length and distance were X. When we started doing calculus, the second term was Y. With X & Y we could shoot a cannon, throw a ball or launch a rocket and fool around with distance, altitude, velocity and acceleration. X was range and Y was elevation. I never worked with Z for elevation in mathematics. I cannot remember a single engineering text where Z meant up.

But I'm not a designer. My guess is the designers' Z-up approach evolved from the 2-D plan drawings. The plan was primary and it was defined as X-Y. Then when elevations entered the picture, Z ended up.

That kinda' makes sense to me but the bottom line, as John Luf puts it, is - no big deal. No big deal to me, but then why did API 610 find reason to switch their coordinate system? I suspect some EN/ISO "standard" is the root.