One or more of several reasons might be at play.
For one thing, Latter-day Saints on the whole and the institutional Church in particular are uncomfortable with, even embarrassed and hypersensitive about, the topic of polygamy, and particularly with pre-Utah polygamy. They find it awkward.
Not only that I wholly believe in my own speculations they wish it would never have happened. I believe they also understand that much of the apparent unseemly side of the introduction of the practice contained is a testimony shaker for some. One must really be convinced that God told Joseph Smith to do this other wise he comes off looking pretty bad in the process.
(Partly, I suspect -- but not entirely -- because of the on-going problem of schismatic polygamist sects.) My own personal preference would be that we be, within the strong constraints of the historical data, more open and forthright about this topic. I think we would be better off all around if we were so.
No doubt. But remember many of the top LDS leaders believe that truths that make the founders look bad are not useful.
Another possible factor is simply that the historical information about Joseph's plural marriages is more than a little murky,
I do not agree with that. It seems we have a lot of information on this especially from many of his plural wives and the 19th century LDS leaders that defended polygamy and it origination with Joseph and this in light of the position of the RLDS that it was from Brigham and not Joseph.
whereas the story of the relationship of Joseph and Emma is much more clear, much more public, and much more relevant to and integrated into the overall historical narrative of Joseph's biography and of formative Church history.
Yet polygamy is a huge issue in Smith's life. To leave it out leaves a huge hole as well as a gap in one of the basis for the doctrine of eternal marriage. Such pass over comments about polygamy, like the one in the intro in the current priesthood/Relief Society manaul seem to border on disingenuous at best.
And I have no doubt that, for good or for ill, the Church website was trying to escape controversy -- which, apart from some small websites such as this one, it has probably largely succeeded in doing.
And preserve tender testimonies that are built on less then full information about the person we are supposed to have a testimony about.