No idea, but this is an intentional decision by the Tolkien Estate.
The text in question has literally only appeared or been referenced in one publication and was not accompanied by any explanation as to its source, the time of composition, the ownership of the manuscript, etc. The only thing that book even says about the source is that it was from Tolkien, still under copyright by the Estate, and translated by H.J. Schütz.
J.R.R. Tolkien, Mîms Klage. © The Executors of J.R.R. Tolkien, 1987. Aus dem Englischen von H.J. Schütz
Nothing else is known about this. It isn't referenced anywhere else, and no one else has even reported having seen the manuscript. Assuming it is genuine it could really be from anywhere. Many of Tolkien's other manuscripts are still unpublished as well.
Jeremy Edmonds of TolkienGuide has reported discussing this poem with the Tolkien Estate and being informed that it was not something they wanted to have published (though seemingly confirming that this is a genuine work).
I’ve spoken at length (previously) with the Estate about this poem. It was made quite clear to me that they still do not want to publish the work in any form outside of the Klett-Cotta Almanac already released
No specific reason has ever been given as to why the Tolkien Estate doesn't want it published. Likewise, no reason is known why Christopher didn't include in HoMe. Seeing as we don't know anything about the context of the original we wouldn't even know which (if any) of the twelve volumes it would even have made sense to put in. Evidently, he either didn't know about it or didn't find it worth including.
Same with Nature of Middle-earth. This text obviously wasn't part of the two manuscript collections that book publishes, and it doesn't fit the theme of the book so it wouldn't really make sense for Hostetter to request to add it in. However in light of the above quote it is possible he did request it and was turned down.