The Royal line of David was not destroyed. In fact Jeremiah , himself.....saw to it....that it was secured! [Jeremiah 43:4-7] "So Johanan son of Kareah and all the army officers and all the people disobeyed the LORD's command to stay in the land of Judah. Instead, Johanan son of Kareah and all the army officers led away all the remnant of Judah who had come back to live in the land of Judah from all the nations where they had been scattered. They also led away all the men, women and children and The king's daughters whom Nebuzaradan commander of the imperial guard had left with Gedaliah son of Ahikam, the son of Shaphan, and Jeremiah the prophet and Baruch son of Neriah. So they entered Egypt in disobedience to the LORD and went as far as Tahpanhes."
In fact, these daughters of the King were Jeremiah's great grand daughters [II Kings 24:18] and [Jeremiah 52:1]. What happened to these Royal daughters of Judah after their escape to Egypt is any body's guess as the scriptures are silent with this regard. But....I suppose they were still young enough to insure that the Royal line was carried on.....that is, if God wanted it to be.
Jeremiah was only one of three different men spoken of in scripture that God fore ordained for a specific task [Jeremiah 1:5]. The other two were "John the Baptist" and "Our Saviour".
Indeed and in addition, Christ's stepfather, Joseph, is descended from David. I'm not quite sure what the author was driving at here. Perhaps he had something else in mind??