The Talmud says:
חכם קודם למלך ישראל חכם שמת אין לנו כיוצא בו מלך ישראל שמת כל ישראל ראוים למלכות -- A Torah Sage comes before the king of Israel, because if a Sage dies, we have no one like him to replace him, but if a king of Israel dies, all of Israel are fit for royalty. [Horayot 13a]
Doesn't a king of the Jews have to descend from King David?