[Jweb_Guru]

While I intuitively like the statistical approach you mention, under it the Born rule holds only approximately, so it should be theoretically possible to observe entangled states which we have never done--i.e. it produces different predictions from the Copenhagen interpretation of quantum mechanics, which means it's not strictly a different interpretation, but its own falsifiable theory. Like I said in another comment, if we ever do observe entangled states directly, people will jump on board one of these alternate explanations like lightning. But until we do, the question of why we never ever observe anything that doesn't look like collapse still needs mathematical justification.