> The idea I've seen proposed was that the wealthy and elite in exile were presented with an opportunity to recover their heritage and homeland if they demonstrated they had a heritage/ Does this sound right?

I'm not qualified to say anything with certainty of course, but from what I know it is pretty clear that the Torah is not a singular, constructed narrative. It is compiled from at least four, relatively easily distinguishable sources who conflict in many aspects of the histories and theologies they present.

Exactly when and why these sources got combined into one text is highly debated, but from what I have heard it likely happened in multiple stages from the destruction of the northern kingdom 720BC onward until -and maybe even after- the babylonian exile. It has not been composed for one specific reason, or at one point in time.

One of the early main reasons could have been to integrate refugees from the north and their culture into the south. Another later on, that most of the traditional leadership in judaism had been destroyed, -the Levites, the house of David and the north-, and the priests of the remaining house of Aaron that ruled during the theocratic phase of judaism, sponsored by the persian kings following the exile, making adjustments to legitimize their power.

One thing that is also rather clear though, is that whatever the Bible says is not a accurate description of the religion of the common people. It's strictly a religious text by and for the political elites of the country, and what they would have liked their countries religion to be. The vast majority of the people could not read it and never visited Jerusalem, much less the Temple, and likely never heard an official priest speak. There are loads of archeological evidence that monotheism and worship in only Jerusalem was not as prevalent as the writers of the bible would like you to believe, for example. They lived their own lives with their own problems, and so they had their own faith apart from whatever the elites were doing. Worship of a female god and wife of Yahweh, Asherah, seems to have been prevalent for quite a while. That makes perfect sense to me: why would a peasant worship a patriarchal god of kingship when his wife is in labor and the rains fail to arrive? He would naturally pray to Asherah for a healthy birth and Baal for the rain instead. That's why the bible condemns such things all the time, because it no doubt happened A LOT.