I do not find the discussion of polygamy interesting. But it is clear by the comments and emails I've received that a number of you do. Without putting the questions I've received into this post I'll explain:
The significance of Joseph's failure to father other children with plural wives is nothing other than a data point in a much larger picture. Fanny Alger was later married to another man and had, as I recall, eight children from that marriage. She was therefore clearly fertile. Joseph fathered children with Emma. He was clearly potent. But between them, Joseph and Fanny had no children although both were clearly capable of doing so had they been determined to bring children to their union.
The many historical candidates and continuing suspicions resulted in an attempt to identify those who may have been a child of Joseph Smith's. There was a decades long search, using DNA testing, to try and prove he fathered someone (anyone) other than Emma's children. None of the suspected children were his. They finished the list about two years ago, as I recall.
This is only significant in one, narrow regard: Joseph's purpose with plural wives was not primarily to produce offspring.
That is very different from what happened under Brigham Young's administration, and later. The primary reason for the later Mormon practice was to produce offspring.
There is something very different to me between Joseph's practice and the later practice. I am not really interested in elaborating fully about the difference. But there was a definite difference in the orientation and justification.
For Joseph, (as has been criticized, condemned and mocked) the explanation dealt with his assurance that the plural marriage would result in "salvation" for not only the wife, but also for "her family." This was/is regarded by many of the critics and even many faithful Latter-day Saints, as Joseph exploiting women using (or abusing) his claim to priesthood power.
What if there was something more to this idea than we have preserved? What if Joseph understood more about salvation that do we? What if Joseph could offer salvation to these others by "sealing" them to himself (he being a saved soul who had a connection to heaven)? What if Joseph was actually offering something of value to these women and to their families, which had little or even nothing to do with producing offspring?
It may just be that Joseph understood this as something quite different than what later became the teaching of the LDS Church.
To me, the subject is plagued with the Brigham Young version of the practice, which almost all Latter-day Saints believe represented an accurate continuation of what Joseph Smith was teaching. I disagree. I think Brigham Young changed rather dramatically the primary orientation. Under Joseph it was primarily focused on the afterlife, salvation and organizing a family that would endure death itself. Under Brigham Young it was primarily focused on breeding children for this life, and secondarily promised some next-life continuation for the worthy.
To me there is much more to the difference between Joseph Smith's focus and Brigham Young's than has been appreciated by those interested in this subject. I think it is possible to view Joseph's practice in different terms than Brigham's. I think it is possible to think of Joseph as morally superior to Brigham Young. I think it is possible to believe Joseph had a higher code of personal conduct than Brigham Young. I think it is possible to believe Joseph held women in higher regard than did Brigham Young.
But this is not a topic I think I need to spend any time sorting through. It really does not interest me. The advocates of polygamy who think they believe in some higher law are almost invariably thinking that Brigham Young got it right and his model is worth following. I think Brigham Young didn't even understand the subject, nor did he have the power to save anyone, nor did connecting to Brigham Young as a sealed plural wife garner any advantage in the world to come.
Some day I may try to fully explain what I think Joseph Smith was up to. But that's not a current priority for me, and I don't think it should be a priority for anyone. At least not until a good deal more of what the restoration was designed to accomplish is first understood.