Nor would it work as a Roman one, but a certain heretical variation did.
Perhaps the most important reason that that happened was that Christianity seperated itself from Judaism. If the early Church had not reached the decision that Gentiles could be Christian without being Jewish, Christianity would never have risen to dominate the Roman Empire.
How hard is it for a sufficiently shell-shocked Xerxes to develop a Persia-compatible version of Judaism? Hell, it was already in development - Persian influence on Judaism was (to my mind, disgustingly) great, including the appearence of an actual dualism in Judaism, as well as the development of angelology.
Both of those factors, dualism and angelology, are highly overestimated as factors of the Jewish religion. They were important, but Judaism has never become a truly dualistic religion in the way that Zoroastrianism and, to a lesser degree, Christianity and Islam have. Nor are angels nearly as important in Judaism as they are in Zoroastrianism, Christianity, and Islam. They form an interesting facet of Judaism and are important in Kabalah, but that is about it.
So perhaps given some more time and/or some master theologician, it is entirely possible to create a Persian Judauism, though ofcourse it would be greatly changed by this.
I am saying it is fully possible for a Iranic form of Judaism to form, it would just have to form into a seperate religion for it to gain any ground beyond a small cult following. Like, say, Christianity.
As for converting people, how hard could it be once you get working on it?
A lot harder than you believe.
If the Judaistic Persian kings remain in power for long enough their faith will spread soon enough. Compare with Shi'ite Islam in OTL Persia (went from the ideology of a small ruling elite to mass religion in less than a century).
Islam is a very different situation. The rise of Islam in Persia involved the Persian nation falling tremendously from power and being conquered by a completely foreign nation. The whole psychology of the Persian people at the time was 180 degrees different from that of Xerxes. Where as Islam was spread among a people who had just suffered one of the greatest falls in human history and thus a people who have lost complete faith in themselves and their traditions. Meanwhile, the conversion of Xerxes-era Persia to an external faith simply makes no sense. They are a people at the height of national egotism. Following something along the lines of the proposed TL it is possible that Xerxes could recieve some sort of vision from G-d (ie the Jewish/Abrahamic G-d) that he interprets as giving him victory and then goes on to construct a Judaeo-Iranic religion. However, for it to go anywhere in converting the Persian people, it would have to fall in line with Iranic theology and, at the same time, appeal to the egotisms rather than asking them, as Judaism does, to redefine themselves as members of a completely different people.
Compare with Christianity in Rome, only take away all persecutions and instead put all the power of the state in its favour.
As I pointed out, conversion of the Roman Empire to Christianity would never have been succesful if Christianity remained a Jewish cult rather than defining itself as something entirely new.
Judaism in Khazaria is a less succesful example, but an example nonetheless and its failure was less the fault of Judaism as a religion and more of Khazaria's conflicting social tendencies.
Khazaria is a completely different situation in terms of national psychology.
Persia is much better off in that regard, its population is fairly concentrated and well-organised, and the cities - where an organised monotheist religion is more likely to catch on - are many and important. This helped Alexander conquer it in OTL - in longer time but more securely, it might allow Judaism to do the same here.
These are all pluses, you're right, and would certainly benefit the rise of an Judaeo-Iranic monotheism. However, national psychology/egotism negate the possibility of Persia not only converting to a new religion, but converting to one not of Iranic origin, and much worse converting to one that demands redefinition of national identity of its converts.
I am not saying it is assured, but I am saying that it could work out just fine.
For all the previous reasons I have layed out, no, it could not work out.
Mind you, a native Persian Abrahamic monotheism would also be quite neat.
And much more plausible.
Funny you should mention Mesopotamia, where I recall in pre-Persian times there existed a (admittedly-small) native Judaistic state. Its name escapes at the moment, though. Still, its a precedent.
Not really. I am not entirely aware of this particular state you speak of, but its existence does not matter. What does matter is that the Babylonians and Assyrians both looked down and oppressed the Jews. Jews were never fond of the Mesopotamians (Babylon even today in Jewish liturgy serves as a symbol of demonic oppression) and the Mesopotamians returned the favor.
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