The Persians sending a small group to a backwater place to create a new ruling religious culture is unheardof. It is hypothesized solely for Judea. If this were just one example of many then fine. However it is an example of nothing rather the product of the imagination.
Who was the audience for any writings? The locals could not read. It was not a creedal religion so details did not count. It was simply a requirement to fulfill the rituals and avoid the taboos. Any writing would be a [i]just so story[/i] as to why we do or do not do these things.
The rationalization goes that while in the (mythical) captivity in Babylon they somehow picked up Persian monotheism. Or at the end of this mythical captivity they were released back to Palestine by Cyrus to promote Persian monotheism in the form of Zoroastrianism. And then -- insert hocus pocus -- the Yahweh story was produced out of Zoroastrianism. The exact details here to not matter as there are at least a dozen imaginative variations upon this idea none of which have the least shred of physical evidence.
But an obvious point is Cyrus was cheated if he got Yahwehism instead of Zoroastrianism and did nothing to correct the matter.
Less obvious is that neither Yahwehism nor Zoroastrianism is monotheist. In fact before this post-captivity fantasy was invented every description of Zoroastrianism was clearly the story of both a good and an evil god with an apocalyptic final days victory of the good guy, Ahura Mazda, the Lord of Light. In any event only if Lucifer or Satan or whatever name is elevated to god status and we ignore he does not lose in the end do we have the remotest connection.
Of course Yahwehism is not monotheist as witnessed by the fact that henotheism had to be invented as a special pleading for the bible to explain the fact that it is not monotheist. The stories of the priests of Yahweh claimed their god, a parallel to the Egyptian Amun, was superior to all other gods, the first god before whom there were no others, but that has nothing to do with the religion of the people. The priests of Yahweh are constantly railing about the people worshiping other gods if you believe the stories.
As to the basic idea of Cyrus the Persian wanting to spread Zoroastrianism there is not the slightest suggestion that it had any particular standing against the other gods of Persia. Nor is there any suggestion of any particular interest of Zoroastrians wanting to spread their religion. Nor is there they least suggestion that this spreading of Zoroastrianism occurred any place else making this a special pleading for bibleland. Thus there is nothing to the entire fantasy.
But this entire fantasy was invented after archaeology conclusively demonstrated nothing older than the mythical return date was real history, no Israel and no David and no anything else, It was part of the desperate attempt to make the OT as old as possible and still pass the giggle test. Nothing new was discovered. It simply became possible to modify religious belief in light of science.
But it is still nonsense. This retreat to a later time of creation of the OT was in response to a popular, public awareness that all the big names like Moses, David and Solomon and their actions were mythical. That was the big news of the time. It was barely mentioned that the absence of evidence applied to everything after the mythical captivity or even that the captivity was a myth. The latter is still not well known today. Today it still has the spurious defenses that once protected belief in Moses and such.