Biblical genealogies serve a very specific purpose. Rather than providing a comprehensive family tree of every lineage, they are carefully curated to introduce individuals who will eventually shape the unfolding narrative.
The primary approach among commentators is that the detailed listing of Uzziel's sons, Mishael, Elzaphan, and Sithri, is entirely practical. These individuals are included because they will step onto the stage of history later in the biblical account. By contrast, the sons of Hebron, the uncle of Moses and Aaron, are completely absent from the record. Since their names are never needed in any future events, they are simply left out.
This selective principle guides the entire genealogical record. The children of Amram are highlighted because Moses, Aaron, and Miriam become the central figures of the era. Similarly, the sons of Izhar are introduced to lay the groundwork for the future rebellion led by Korah. The sons of Aaron, along with Phinehas the son of Eleazar, are also recorded in anticipation of the vital roles they will fulfill. On the other hand, the descendants of Ithamar are omitted for the exact same reason as the sons of Hebron. Without any further mention or active role in the events to come, they are left out of the narrative framework.