For me that paradox just means that you can't just assume distribution of calculated property because (a)symmetries of the calculation will bite you in the ass.

Same thing that you can't just : "I don't know. Therefore 50/50."

The whole quantum thing angle doesn't make much sense to me because noone assumes there's some distribution of derived properties. Whole qm is as I understand it, calculating those distribution from underlying (a)symmetries of the model.