and because classical approximations provide numbers rather than operators! Otherwise one never leaves the quantum domain and cannot make contact to the classical concepts in the description of experimental arrangements.This is just, because the classical approximations are accurate enough for these purposes
Maybe not necessary but conspicuously present everywhere.(though the item concerning the Born-Oppenheimer approximation in solid-state physics is not always applicable). Nothing in this proves the necessity of a Heisenberg cut.
It is the dichotomy in the description used, not in the world itself!It's hard to accept for Copenhagenianers, but there's no hint at the claimed dichotomy between a classical and a quantum world.