Yeah that's it, Sauron just was not so important for the stories presented in Sil, as well as the Mouth was not so important for the story. In this way, Tom, Bert and William were more important than Mouth of Sauron in the story. But you can't forget that there are another thousands of people in the Middle-Earth whose actions had strong impact even in the large view, but they are scarcely mentioned. And there were thousands of people who lived their lives and did many things. For example, if we had a story of the fall of Ost-in-Edhil, I can bet that we'll all know about the famous Elven Smith, who was in very high rank, gave good advices to Celebrimbor, and he even was at first against the agreement with Sauron. He was a good and funny fellow, and in the end, he was slain by Sauron himself on the stairs to the House of Mírdain when covering Celebrimbor's escape, which even though was in vain eventually in the end. And we will all know his name and remember him as one of the great heroes in the "hall of fame". Now, since no one wrote the story, we have no knowing of such a person.
Note: I hope you understand that this person never truly existed. There is no mention of such a person in all Tolkien's works. I totally made it up just for purposes of this post and any resemblance to actual persons in Tolkien's work, living or dead, is purely coincidential 