I've always seen the standard interpretation and axioms of QM as in some way tricky on a philosophical level. They state the collapse of the wave function is caused by the measurement.
3.b If $A$ is an observable with eigenvalues $a_k$ and eigenvectors $|k\rangle$ $(A|k\rangle = ak|k\rangle$), given a system in the state $|\psi\rangle$, the probability of obtaining $a_k$ as the outcome of the measurement of $A$ is $p(a_k) = |\langle k | \psi \rangle|^2$. After the measurement the system is left in the state projected on the subspace of the eigenvalue $a_k$ (wave function collapse)
I've known the general consensus is that the collapse of the wave function is a manifestation of a more general process called decoherence. So in the standard interpretation, the wave function seems to collapse due to the environment, but it really collapses due to the measurement. Maybe because in the first experiments of the physicists of the 20th century the measurement apparatus caused the collapse of the wave function, so it might have seemed the best way to define those axioms..
Why don't we use the decoherence process as an axiom somehow? In this way, we might avoid some misinterpretation of quantum mechanics and have a deeper understanding of the subject.