But [according to byrne] to be considered for priestly office [particulary function of temple high priest], it was not suffcient for a man to be born a cohen. He had to be a first--born son of a cohen.
You have posed some interesting ideas, but maybe we only have to look at the Bible to find the answers. It seems, in the history of kingship and the high priesthood in Israel and Judah, there were only a few instances of the king also being the high priest. Examples of this should be easy to find. And, it seems, this was also considered the best of all worlds to many or most Israelites. But, again, it seemed to be rare.
As regards children, we can also look at the examples provided in the Bible as regards succession to the posts. It seems it was not just the house of the father that was important but possibly the strength of the house of the mother was at least equally or more important than that of the father. The passing on of the "birthright" of the father, was not always given to the first born obviously. See Abraham, Isaac, Joseph, Solomon, etc. And, even more interestingly the birth right of Moses, seems to have been bypassed entirely. Possibly he had no wife with the proper background to take over his place? Even more interesting, is that in current Judiasm, the act of being born Jewish is the religion or "race" of the mother being a Jew, the nationality or race of the father is of no importance. Jewishness is passed on by a Jewish mother only.
This probably explains why so many Israelit/Kings of Israel and or Judah, etc., were protected by mercenaries, and not by loyal Jews! Certainly King David and Solomon, etc., never counted upon their fellow Jews to protect them or fight their wars or at least to be the generals of their armies!
This entire thing is a bag of worms, and one wonders if it can ever be explained to any certainty!
© Charles N. Pope, US Library of Congress. All rights reserved.