The people of Israel and Judah seemed to have been scrupulous in their record keeping. Although not all the genealogies in this part of Chronicles are complete, and not all extended to the exile (some tribes seem to have faded away, or been exiled to Assyria before the Babylonian exile), they provide a record as it was known at the time.
1 Chronicles 9:1 So all Israel was listed in the genealogical records in The Book of the Kings of Israel.
At a practical level, it became important when the exiles (their descendants) were allowed to return to Israel, in particular Jerusalem. It was also a link to their claim on the land, establishing a legitimacy for priests and tribal leaders.