But its unnaturalness has to do with the way we are constructed. Nature doesn't come pre-equipped with a list of the right macroproperties.

It seems likely to me that the the laws of motion governing the time evolution of microstates has something to do with determining the "right" macroproperties -- that is, the ones that lead to reproducible states and processes on the macro scale. (Something to do with coarse-graining, maybe?) Then natural selection filters for organisms that take advantage of these macro regularities.