Mdd, it is a conditional mitzva. Here is the language of the Netziv (He’emek Devar Devarim 17,14):
???, ??? ???? ?? ??? ????? ???? ?? ????? ?????? ????? ??? ??? ????, ??? ‘????? ????? ???’; ???? ???? ????? ??”? ?????? ????? ???! ??? ??, ??? ???? ‘?????’?
?????, ????? ?????? ?????? ?????, ?? ????? ?? ?? ??? ????? ?? ?? ?? ??? ??? ????????, ??? ????? ????? ????? ????? ??? ?????, ??? ????? ???? ??? ??? ??? ?????? ??? ??????, ???? ?? ?? ???? ????? ?? ?? ????? ???, ???? ?????? ????? ?????? ???? ???? ????? ????? ????? ????? ???, ???? ??? ?? ???? ????? ????? ????? ???, ?? ??? ??? ??? ?????? ??? ????? ??? ???, ?? ?? ?????? ?????? ??? ????????? ??????? ???? ???? ????, ?? ?? ????? ??? ???????? ????? ???.
As for David and his descendants, statistically all of us are probably his descendants. Only cohanim and levi’im are definitely not through a continuous line of males. Moreover, Rambam says that a son only inherits his father’s position if he is like him in yirat Shemayim (Hilchot Melachim 1,7).