Inferring the statistical interpretation of quantum mechanics from the classical limit

It is widely believed that the statistical interpretation of quantum mechanics cannot be inferred from the Schrödinger equation itself, and must be stated as an additional independent axiom. Here I propose that the situation is not so stark. For systems that have both continuous and discrete degrees of freedom (such as coordinates and spin respectively), the statistical interpretation for the discrete variables is implied by requiring that the system's gross motion can be classically described under circumstances specified by the Schrödinger equation. However, this is not a full-fledged derivation of the statistical interpretation because it does not apply to the continuous variables of classical mechanics.