That is a somewhat narrow definition of "why", I'd say. But indeed, the transition from quantum mechanics to classical mechanics is unclear.

There are several interpretations of quantum mechanics, but they are empirically equivalent, so you can just pick your favourite and move on. That's not necessarily a big mystery. The math works, as you say, and that's the whole point of a physical theory.

There are also several interpretations of statistics. Does that mean we don't understand "why" a dice rolls results with a certain frequency?

Note that superconductivity and the quantum Hall effect are both macroscopic quantum effects, so we do know what a macroscopic quantum system looks like.