Asking why Batman has never killed the Joker, ignores the question of "Why has Superman never killed Luthor?" or "Why has Wonder Woman never killed Ares?". Joker may be one of the biggest foes and threats in all of DC, but compared to the other major villains and archenemies, Joker's probably the weakest of them. Yet no one complains when Superman spares Luthor or Wonder Woman spares Ares. No one complains when Green Lantern spares Sinestro, and no one cares when Aquaman spares Black Manta... even though he has every right to kill Manta, for killing his son.
So why do you think Batman's always the one who gets complaints for sparing the weakest of the major DC villains?