[Moderator's note: Spin off from previous thread since this is a separate topic from that one.]
It's hard to expect that it ever gets a standard interpretation, because it contradicts the very observations which lead to the discovery of modern quantum including Born's probability interpretation of the wave function (i.e., pure states): We do not find smeared distributions when we deal with single quanta (particles or photons) nor do we measure expectation values, if the measurement device is not constructed such that it does so. We rather measure what QT predicts: E.g., when measuring the position of an electron, prepared in some state, we find single pointlike hits (within the spatial resolution of the detector), with the single outcomes being random and distributed according to the probabilities predicted by QT (within the spatial resolution of the detector again).But the thermal interpretation is not (yet?) a standard interpretation. I do agree that what you say would likely be true of an interpretation that solves the measurement problem (eg. maybe something like Bohmian Mechanics or the thermal interpretation, but that is also not a standard interpretation at this time).
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