Rather, its random characterization seems to imply a lack of knowledge about 'what is going on in Nature'. Nature's 'choice', in my view is to support the global pattern of vibration frequency of all matter and all fields. It is holistic and unified, until some organism tries to experience the world through some experiential symmetry breaking. Organism experience, through 'natural quantum measurement' breaks the invariance symmetry of this global pattern. This might be called a Dirac choice on the part of organism quantum observers.
Entanglement is a form of coherence of matter waves over large space-time intervals.
For example, two photons, emitted in opposite directions during a double-photon emission, retain their matter wave coherence. They are still in a potentiality context. They are, in fact, a single quantum system, even if the system is spread over huge space-time distances. The convention of retaining the particle language by distinguishing two particle photons is misleading in this quantum field situation. This misapprehension is what leads to the apparent quantum weirdness.